Tootfinder

Isosystolic Inequalities for Holomorphic Chains in $\mathbb{C}P^{n}$
Luciano L. Junior
https://arxiv.org/abs/2507.23156 https://arxiv.org/pdf/2507.23156

Isosystolic Inequalities for Holomorphic Chains in $\mathbb{C}P^{n}$
We introduce the \emph{holomorphic $k$-systole} of a Hermitian metric on $\mathbb{C}P^n$, defined as the infimum of areas of homologically non-trivial holomorphic $k$-chains. Our main result establishes that, within the set of Gauduchon metrics, the Fubini-Study metric locally minimizes the volume-normalized holomorphic $(n-1)$-systole. As an application, we construct Gauduchon metrics on $\mathbb{C}P^2$ arbitrarily close to the Fubini-Study metric whose homological $2$-systole is realized by n…

A holomorphic Kolmogorov-Arnold network framework for solving elliptic problems on arbitrary 2D domains
Matteo Calaf\`a, Tito Andriollo, Allan P. Engsig-Karup, Cheol-Ho Jeong
https://arxiv.org/abs/2507.22678

A holomorphic Kolmogorov-Arnold network framework for solving elliptic problems on arbitrary 2D domains
Physics-informed holomorphic neural networks (PIHNNs) have recently emerged as efficient surrogate models for solving differential problems. By embedding the underlying problem structure into the network, PIHNNs require training only to satisfy boundary conditions, often resulting in significantly improved accuracy and computational efficiency compared to traditional physics-informed neural networks (PINNs). In this work, we improve and extend the application of PIHNNs to two-dimensional proble…

Quadratic forms of holomorphic cusp forms and the decay of their $\ell^p$-norms for $0 < p < 2$
Shenghao Hua
https://arxiv.org/abs/2507.21951 https://

Quadratic forms of holomorphic cusp forms and the decay of their $\ell^p$-norms for $0 < p < 2$
In this paper, we demonstrate that, given an orthonormal basis of holomorphic Hecke cusp forms, conditionally, quadratic forms composed of cusp forms -- each expressed as a bounded linear combination of holomorphic Hecke cusp forms -- are generally not themselves expressible as bounded linear combinations of holomorphic Hecke cusp forms when the sum of the weights exceeds some absolute constant, provided that the coefficients of the quadratic form satisfy appropriate nonvanishing and boundednes…

Holomorphic 1-forms without zeros on K\"ahler threefolds
Simon Pietig
https://arxiv.org/abs/2506.22067 https://arxiv.org/pdf/250…

Holomorphic 1-forms without zeros on Kähler threefolds
We classify all smooth compact connected Kähler threefolds that admit the structure of a $C^\infty$-fiber bundle over the circle. This generalizes the work of Hao and Schreieder in the projective case. In contrast to the projective case, there cannot always exist a smooth morphism to a positive-dimensional torus. Instead, we show that such a compact Kähler threefold admits a finite étale cover that is bimeromorphic to a $\mathbb{P}^1$-, $\mathbb{P}^2$-, or Hirzebruch surface-bundle over a lo…

A linear topological invariant for weighted spaces of holomorphic functions
Andreas Debrouwere, Quinten Van Boxstael
https://arxiv.org/abs/2506.23695 https…

A linear topological invariant for weighted spaces of holomorphic functions
We study the linear topological invariant $(Ω)$ for a class of Fréchet spaces of holomorphic functions of rapid decay on strip-like domains in the complex plane, defined via weight function systems. We obtain a complete characterization of the property $(Ω)$ for such spaces in terms of an explicit condition on the defining weight function systems. As an application, we investigate the surjectivity of the Cauchy-Riemann operator on certain weighted spaces of vector-valued smooth functions.

Julia directions for holomorphic curves
Alexandre Eremenko
https://arxiv.org/abs/2507.21780 https://arxiv.org/pdf/2507.21780…

Julia directions for holomorphic curves
A theorem of Picard's type is proved for entire holomorphic mappings into complex projective varieties. This theorem has local character in the sense that the existence of Julia directions can be proved under a natural additional assumption. An example is given which shows that Borel's theorem on holomorphic curves omitting hyperplanes does not have such a local counterpart.

Universal embeddings of flag manifolds and rigidity phenomena
Andrea Loi, Roberto Mossa, Fabio Zuddas
https://arxiv.org/abs/2507.23606 https://arxiv.org/pd…

Universal embeddings of flag manifolds and rigidity phenomena
We prove a universal embedding theorem for flag manifolds: every flag manifold admits a holomorphic isometric embedding into an irreducible classical flag manifold. This result generalizes the classical celebrated embedding theorems of Takeuchi [30] and Nakagawa-Takagi [27]. Using this embedding, we establish new rigidity phenomena for holomorphic isometries between homogeneous Kähler manifolds. As a first immediate consequence we show the triviality of a Kähler-Ricci soliton submanifod of $C…

Non-holomorphic modular flavor symmetry and odd weight polyharmonic Maa{\ss} form
Bu-Yao Qu, Jun-Nan Lu, Gui-Jun Ding
https://arxiv.org/abs/2506.19822 http…

Non-holomorphic modular flavor symmetry and odd weight polyharmonic Maaß form
We extend the framework of non-holomorphic modular flavor symmetry to include the odd weight polyharmonic Maaß forms. The integer weight polyharmonic Maaß forms of level $N$ can be arranged into multipltets of the homogeneous finite modular group $Γ'_N$. We propose to construct the integer weight, including weight one, non-holomorphic polyharmonic Maaß forms from the non-holomorphic Eisenstein series. The previous results of even weight polyharmonic Maaß forms are reproduced. We apply this…

Holomorphic Unified Field Theory of Gravity and the Standard Model
John. W. Moffat, Ethan. J. Thompson
https://arxiv.org/abs/2506.19161 https://

Holomorphic Unified Field Theory of Gravity and the Standard Model
We present a holomorphic framework in which gravity, gauge interactions, and their couplings to charges and currents emerge from a single geometric action on a four-complex-dimensional manifold. The Hermitian metric yields on the real slice $y^μ= 0$, a real symmetric metric $g_{(μν)}$ giving the vacuum Einstein equations, and an antisymmetric part $g_{[μν]}$ that reproduces Maxwell's equations with sources. A single holomorphic gauge connection for $G_{\text{GUT}}$, such as $SU(5)$ or $SO(…

Gromov-Witten invariants of log Calabi-Yau 3-folds are holomorphic lagrangian correspondences
Brett Parker
https://arxiv.org/abs/2506.20092 https://…

Gromov-Witten invariants of log Calabi-Yau 3-folds are holomorphic lagrangian correspondences
We introduce a holomorphic version of Weinstein's symplectic category, in which objects are holomorphic symplectic manifolds, and morphisms are holomorphic lagrangian correspondences. We then extend this category to log schemes, and prove that Gromov-Witten invariants of log Calabi-Yau 3-folds are naturally encoded as holomorphic lagrangian correspondences. Gromov-Witten invariants and Donaldson-Thomas invariants are then conjecturally related by a natural unitary lagrangian correspondence.

A Schwarz-Jack lemma, circularly symmetric domains and numerical ranges
Javad Mashreghi, Annika Moucha, Ryan O'Loughlin, Thomas Ransford, Oliver Roth
https://arxiv.org/abs/2506.23831

A Schwarz-Jack lemma, circularly symmetric domains and numerical ranges
We prove a Schwarz-Jack lemma for holomorphic functions on the unit disk with the property that their maximum modulus on each circle about the origin is attained at a point on the positive real axis. With the help of this result, we establish monotonicity and convexity properties of conformal maps of circularly symmetric and bi-circularly symmetric domains. As an application, we give a new proof of Crouzeix's theorem that the numerical range of any $2\times 2$ matrix is a $2$-spectral set for t…

Polynomial stability conditions for vector bundles: Positivity, equivariance and blow-ups
R\'emi Delloque, Achim Napame, Carlo Scarpa, Carl Tipler
https://arxiv.org/abs/2506.23842

Polynomial stability conditions for vector bundles: Positivity, equivariance and blow-ups
We introduce the notion of P-critical connections for hermitian holomorphic vector bundles over compact balanced manifolds: integrable hermitian connections whose curvature solves a polynomial equation. Such connections include HYM and dHYM connections, as well as solutions to higher rank Monge-Ampère or J-equations, and are a slight generalisation of Dervan-McCarthy-Sektnan's Z-critical connections motivated by Bayer's polynomial Bridgeland stability conditions. The associated equations come …

A note on the boundary dynamics of holomorphic iterated function systems
Argyrios Christodoulou
https://arxiv.org/abs/2507.16358 https://

A note on the boundary dynamics of holomorphic iterated function systems
We consider the boundary dynamics of iterated function systems of holomorphic self-maps of the unit disc. Our main result provides a sufficient condition which guarantees that the dynamical behaviour of a left iterated function system in the interior of the unit disc can be extended to the boundary. This generalises an extension of the classical Denjoy--Wolff Theorem, due to Bourdon, Matache and Shapiro, to the setting of iterated function systems. To do so we modify estimates for the Hardy nor…

A Selberg-type zero-density result for twisted $\rm GL_2$ $L$-functions and its application
Qingfeng Sun, Hui Wang, Yanxue Yu
https://arxiv.org/abs/2505.23573

A Selberg-type zero-density result for twisted $\rm GL_2$ $L$-functions and its application
Let $f$ be a fixed holomorphic primitive cusp form of even weight $k$, level $r$ and trivial nebentypus $χ_r$. Let $q$ be an odd prime with $(q,r)=1$ and let $χ$ be a primitive Dirichlet character modulus $q$ with $χ\neqχ_r$. In this paper, we prove an unconditional Selberg-type zero-density estimate for the family of twisted $L$-functions $L(s, f \otimes χ)$ in the critical strip. As an application, we establish an asymptotic formula for the even moments of the argument function $S(t, f…

On multidimensional Bohr radius of finite dimensional Banach spaces
Vasudevarao Allu, Subhadip Pal
https://arxiv.org/abs/2506.23540 https://

On multidimensional Bohr radius of finite dimensional Banach spaces
In this paper, we improve the lower estimate of multidimensional Bohr radius for unit ball of $\ell^n_q$-spaces ($1\leq q\leq \infty$) for bounded holomorphic functions with values in finite dimensional complex Banach spaces. The new estimate provides the improved lower bound for the Bohr radius which was previously given by Defant, Maestre, and Schwarting [Adv. Math. 231 (2012), 2837--2857].

Invariant measures on moduli spaces of twisted holomorphic 1-forms and strata of dilation surfaces
Paul Apisa, Nick Salter
https://arxiv.org/abs/2507.10685

Invariant measures on moduli spaces of twisted holomorphic 1-forms and strata of dilation surfaces
The moduli space of twisted holomorphic 1-forms on Riemann surfaces, equivalently dilation surfaces with scaling, admits a stratification and GL(2,R)-action as in the case of moduli spaces of translation surfaces. We produce an analogue of Masur-Veech measure, i.e. an SL(2,R)-invariant Lebesgue class measure on strata or explicit covers thereof. This relies on a novel computation of cohomology with coefficients for the mapping class group. The computation produces a framed mapping class group i…

Definability of complex functions in o-minimal structures
Adele Padgett, Patrick Speissegger
https://arxiv.org/abs/2506.15119 https://

Definability of complex functions in o-minimal structures
We prove that some holomorphic continuations of functions in the classes $\mathbf{an}^*$ and $\mathcal{G}$ are definable in the o-minimal structures $\mathbb{R}_{\mathrm{an}^*}$ and $\mathbb{R}_{\mathcal{G}}$ respectively. More specifically, we give complex domains on which the holomorphic continuations are definable, and show they are optimal. As an application, we describe optimal domains on which the Riemann $ζ$ function is definable in o-minimal expansions of $\mathbb{R}_{\mathrm{an}^*,\ex…

Untriangular factorization of holomorpic symplectic matrices
Gaofeng Huang, Frank Kutzschebauch, Phan Quoc Bao Tran
https://arxiv.org/abs/2507.18963 https://

Untriangular factorization of holomorpic symplectic matrices
We prove that every holomorphic symplectic matrix can be factorized as a product of holomorphic unitriangular matrices with respect to the symplectic form $ \left[\begin{array}{ccc} 0 & L_n \\ -L_n & 0\end{array}\right]$ where $L$ is the $n \times n$ matrix with $1$ along the skew-diagonal. Also we prove that holomorphic unitriangular matrices with respect to this symplectic form are products of not more than $7$ holomorphic unitriangular matrices with respect to the standard symplectic form $\…

Resurgent Lambert series with characters
David Broadhurst, Daniele Dorigoni
https://arxiv.org/abs/2507.21352 https://arxiv.org/pdf/2507.21352

Resurgent Lambert series with characters
We consider certain Lambert series as generating functions of divisor sums twisted by Dirichlet characters and compute their exact resurgent transseries expansion near $q=1^-$. For special values of the parameters, these Lambert series are expressible in terms of iterated integrals of holomorphic Eisenstein series twisted by the same characters and the transseries representation is a direct consequence of the action of Fricke involution on such twisted Eisenstein series. When the parameters of …

Holomorphic parabolic geometries on smooth projective varieties
Benjamin McKay
https://arxiv.org/abs/2507.15691 https://arxiv.org/pdf…

Holomorphic parabolic geometries on smooth projective varieties
We classify the holomorphic parabolic geometries on compact complex manifolds of general type. We accomplish this by bounding the numerical dimension of any smooth projective variety in terms of geometric invariants of the flag variety model of any holomorphic parabolic geometry on that variety. Along the way, we uncover foliations and fibrations on smooth projective varieties that admit holomorphic parabolic geometries.

Finite Nonlocal Holomorphic Unified Quantum Field Theory
J. W. Moffat, E. J. Thompson
https://arxiv.org/abs/2507.14203 https://arxiv.…

Finite Nonlocal Holomorphic Unified Quantum Field Theory
In this paper the non-local finite quantum-gravity framework is incorporated into the Complex non-Riemannian Holomorphic Unified Field Theory formulated on a complexified four-dimensional manifold. By introducing entire-function regulators $F(\Box) = \exp\!\bigl(\Box / M_*^2\bigr)$ into the holomorphic Einstein-Hilbert action, we achieve perturbative UV finiteness at all loop orders, while preserving BRST invariance and holomorphic gauge symmetry. We derive the modified gauge-gravity coupling s…

Exceptional points and defective resonances in an acoustic scattering system with sound-hard obstacles
Kei Matsushima, Takayuki Yamada
https://arxiv.org/abs/2506.19229

Exceptional points and defective resonances in an acoustic scattering system with sound-hard obstacles
This paper is concerned with non-Hermitian degeneracy and exceptional points associated with resonances in an acoustic scattering problem with sound-hard obstacles. The aim is to find non-Hermitian degenerate (defective) resonances using numerical methods. To this end, we characterize resonances of the scattering problem as eigenvalues of a holomorphic integral operator-valued function. This allows us to define defective resonances and associated exceptional points based on the geometric and al…

Inverse conductivity problem on a Riemann surface
Peter L. Polyakov
https://arxiv.org/abs/2506.23362 https://arxiv.org/pdf/2506.23362…

Inverse conductivity problem on a Riemann surface
We present an application of the Faddeev-Henkin exponential ansatz and of the d-to-d-bar map on the boundary to inverse conductivity problem on a bordered Riemann surface in CP2. In our approach we use integral formulas for operator d-bar developed in [HP1]-[HP4] and integral formulas for holomorphic functions on Riemann surfaces from [P].

This https://arxiv.org/abs/2412.07849 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Archimedean zeta functions, singularities, and Hodge theory
We use Hodge theory to relate poles of the Archimedean zeta function $Z_f$ of a holomorphic function $f$ with several invariants of singularities. First, we prove that the largest nontrivial pole of $Z_f$ is the negative of the minimal exponent of $f$, whose order is determined by the multiplicity of the corresponding root of the Bernstein--Sato polynomial $b_f(s)$, resolving in a strong sense a question of Mustaţă--Popa. This simultaneously generalizes a result of Loeser for isolated singula…

This https://arxiv.org/abs/2504.09383 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Numerical Calculation of Periods on Schoen's Class of Calabi-Yau Threefolds
Through classical modularity conjectures, the period integrals of a holomorphic $3$-form on a rigid Calabi-Yau threefold are interesting from the perspective of number theory. Although the (approximate) values of these integrals would be very useful for studying such relations, they are difficult to calculate and generally not known outside of the rare cases in which we can express them exactly. In this paper, we present an efficient numerical method to compute such periods on a wide class of…

On two versions of holomorphic quantum plane
Oleg Aristov
https://arxiv.org/abs/2507.14490 https://arxiv.org/pdf/2507.14490

On two versions of holomorphic quantum plane
We find power series descriptions of two versions of holomorphic quantum plane, the Arens--Michael envelope and the envelope with respect to the class of Banach PI algebras, in the case of non-unitary parameter.

Non-holomorphic Contributions in GMSB with Adjoint Messengers
Busra Nis, Cem Salih Un
https://arxiv.org/abs/2507.07970 https://arxiv.…

Non-holomorphic Contributions in GMSB with Adjoint Messengers
We consider models of gauge mediated supersymmetry breaking, in which the breaking is transmitted to the visible sector by the messenger fields from the adjoint representation of MSSM's gauge group. We include the non-holomorphic terms induced by the supersymmetry breaking and involve them in the renormalization group evolution. The main impact from the non-holomorphic terms arises in the right-handed stau mass, which requires large hypercharge interactions with the messengers to accommodate no…

Bounded $H^\infty$-calculus for vectorial-valued operators with Gaussian kernel estimates
Davide Addona, Vincenzo Leone, Luca Lorenzi, Abdelaziz Rhandi
https://arxiv.org/abs/2507.16368

Bounded $H^\infty$-calculus for vectorial-valued operators with Gaussian kernel estimates
We prove that the vector-valued generator of a bounded holomorphic semigroup represented by a kernel satisfying Gaussian estimates with bounded $H^\infty$-calculus in $L^2(\mathbb R^d;\mathbb C^m)$ admits bounded $H^\infty$-calculus for every $p\in (1,\infty)$. We apply this result to the elliptic operator $-{\rm div}(Q\nabla)+V$, where the potential term V is a matrix-valued function whose entries belong to $L^1_{\rm loc}(\mathbb R^d)$ and, for almost every $x\in \mathbb R^d$, $V(x)$ is a symm…

Bounded Pluriharmonic Functions and Holomorphic Functions on Teichm\"uller Space II -- Poisson integral formula --
Hideki Miyachi
https://arxiv.org/abs/2507.19930 https://

Bounded Pluriharmonic Functions and Holomorphic Functions on Teichmüller Space II -- Poisson integral formula --
In this paper, we establish the Poisson integral formula for bounded pluriharmonic functions on the Teichmüller space of analytically finite Riemann surfaces of type $(g,m)$ with $2g-2+m>0$. We also discuss a version of the F. and M. Riesz theorem concerning the value distribution of plurisubharmonic functions on the Teichmüller space, as well as a Teichmüller-theoretic interpretation of the mean value theorem for pluriharmonic functions.

A criterion for holomorphic Lie algebroid connections
David Alfaya, Indranil Biswas, Pradip Kumar, Anoop Singh
https://arxiv.org/abs/2506.10514 https://

A criterion for holomorphic Lie algebroid connections
Given a holomorphic Lie algebroid $(V, ϕ)$ on a compact connected Riemann surface $X$, we give a necessary and sufficient condition for a holomorphic vector bundle $E$ on $X$ to admit a holomorphic Lie algebroid connection. If $(V, ϕ)$ is nonsplit, then every holomorphic vector bundle on $X$ admits a holomorphic Lie algebroid connection for $(V, ϕ)$. If $(V, ϕ)$ is split, then a holomorphic vector bundle $E$ on $X$ admits a holomorphic Lie algebroid connection if and only if the degree of e…

Embedding $\mathrm{SL}(2,\mathbb{C})/\mathbb{Z}_2$ in Complex Riemannian Geometry
John. W. Moffat, Ethan. J. Thompson
https://arxiv.org/abs/2506.19158 http…

Embedding $\mathrm{SL}(2,\mathbb{C})/\mathbb{Z}_2$ in Complex Riemannian Geometry
We present a unified framework demonstrating how the spinor complex Lorentz group SL(2,C)/Z\_2 is realized as a canonical subgroup within a four-dimensional complex Riemannian manifold. Building on the complex, holomorphic metric extension and contour-integration regularization of classical singularities, we show that promoting the metric to a complex-valued tensor on a complex 4-fold enlarges the frame bundle to SO(4,C). Its spin double cover factorizes as a product of two independent SL(2,C) …

This https://arxiv.org/abs/2411.16261 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Almost-Fuchsian representations in PU(2,1)
In this paper, we study nonmaximal representations of surface groups in PU(2,1). In genus large enough, we show the existence of convex-cocompact representations of non-maximal Toledo invariant admitting a unique equivariant minimal surface, which is holomorphic and almost totally geodesic. These examples can be obtained for any Toledo invariant of the form 2-2g +2/3 d, provided g is large compared to d. When d is not divisible by 3, this yields examples of convex-cocompact representations in P…

This https://arxiv.org/abs/2209.08741 has been replaced.
link: https://scholar.google.com/scholar?q=a

Bergman representative coordinate, constant holomorphic curvature and a multidimensional generalization of Carathéodory's theorem
By using the Bergman representative coordinate and Calabi's diastasis, we extend a theorem of Lu to bounded pseudoconvex domains whose Bergman metric is incomplete with constant holomorphic sectional curvature. We characterize such domains that are biholomorphic to a ball possibly less a relatively closed pluripolar set. We also provide a multidimensional generalization of Carathéodory's theorem on the continuous extension of the biholomorphisms up to the closures. In particular, sufficient co…

The Rhaly Operators on K\"othe Spaces
Nazl{\i} Do\u{g}an
https://arxiv.org/abs/2507.20214 https://arxiv.org/pdf/2507.20214

The Rhaly Operators on Köthe Spaces
We introduce and study the Rhaly operator on Köthe spaces, with a primary focus on understanding its well-definedness, continuity, and compactness. We especially examine operators acting on power series spaces of both infinite and finite type. In the sequel, we provide integral representations for the Rhaly operator on the space of entire functions $H(\mathbb{C})$ and the space of holomorphic functions on the unit disc $H(\mathbb{D})$. We also investigate the topologizability and power bounded…

Unknottedness of symplectic submanifold fillings
Zhengyi Zhou
https://arxiv.org/abs/2506.06807 https://arxiv.org/pdf/2506.06807

Unknottedness of symplectic submanifold fillings
We show that any symplectic filling of the standard contact submanifold $(\mathbb{S}^{2n-1},ξ_{\mathrm{std}})$ of $(\mathbb{S}^{2n+1},ξ_{\mathrm{std}})$ in $(\mathbb{D}^{n+1},ω_{\mathrm{std}})$ is smoothly unknotted if $n\ge 2$. We also give a self-contained proof of the Siefring intersection formula between punctured holomorphic curves and holomorphic hypersurfaces used in the proof using the $L$-simple setup of Bao-Honda.

Finite energy foliations in the restricted three-body problem
Lei Liu, Pedro A. S. Salom\~ao
https://arxiv.org/abs/2506.17867 https://

Finite energy foliations in the restricted three-body problem
This paper is about using pseudo-holomorphic curves to study the circular planar restricted three-body problem. The main result states that for mass ratios sufficiently close to $\frac{1}{2}$ and energies slightly above the first Lagrange value, the flow on the regularized component $\mathbb R P^3 \# \mathbb R P^3$ of the energy surface admits a finite energy foliation with three binding orbits, namely two retrograde orbits around the primaries and the Lyapunov orbit in the neck region about th…

Inverse Seesaw Model in Non-holomorphic Modular $A_4$ Flavor Symmetry
Xianshuo Zhang, Yakefu Reyimuaji
https://arxiv.org/abs/2507.06945 https://

Inverse Seesaw Model in Non-holomorphic Modular $A_4$ Flavor Symmetry
We investigate an inverse seesaw model of neutrino masses based on non-holomorphic modular $A_4$ symmetry, by extending the framework of modular-invariant flavor models beyond the conventional holomorphic paradigm. After establishing the general theoretical framework, we analyze three concrete model realizations distinguished by their $A_4$ representation assignments and modular weight configurations for the matter fields. Focusing on these three specific realizations, we perform a comprehensiv…

Monotonicity properties of hyperbolic projections in holomorphic iteration
Argyrios Christodoulou, Konstantinos Zarvalis
https://arxiv.org/abs/2506.19562 h…

Monotonicity properties of hyperbolic projections in holomorphic iteration
We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, necessary, assumptions, the projections exhibit monotonicity properties akin to those present in continuous dynamics. Our techniques are purely hyperbolic-geometric in nature and provide the general framework for analysing projections of arbitrary sequences onto curves.

Holomorphic supergravity in ten dimensions and anomaly cancellation
Anthony Ashmore, Javier Jos\'e Murgas Ibarra, Charles Strickland-Constable, Eirik Eik Svanes
https://arxiv.org/abs/2507.06003

Holomorphic supergravity in ten dimensions and anomaly cancellation
We formulate a ten-dimensional version of Kodaira-Spencer gravity on a Calabi-Yau five-fold that reproduces the classical Maurer-Cartan equation governing supersymmetric heterotic moduli. Quantising this theory's quadratic fluctuations, we show that its one-loop partition function simplifies to products of holomorphic Ray-Singer torsions and exhibits an anomaly that factorises as in $SO(32)$ and $E_8\times E_8$ supergravity. Based on this, we conjecture that this theory is the $SU(5)$-twisted v…

Replaced article(s) found for gr-qc. https://arxiv.org/list/gr-qc/new
[2/2]:
- Holomorphic Unified Field Theory of Gravity and the Standard Model
John. W. Moffat, Ethan. J. Thompson

Replaced article(s) found for physics.gen-ph. https://arxiv.org/list/physics.gen-ph/new
[1/1]:
- Top Quark Bound States in Finite and Holomorphic Quantum Field Theories
E. J. Thompson

Replaced article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- Holomorphic null curves in the special linear group
Antonio Alarcon, Jorge Hidalgo

On the reachable space for parabolic equations
Sylvain Ervedoza (IMB), Adrien Tendani-Soler (ICB)
https://arxiv.org/abs/2507.15407 https://

On the reachable space for parabolic equations
In this article, we provide a description of the reachable space for the heat equation with various lower order terms, set in the euclidean ball of $\mathbb{R}^d$ centered at $0$ and of radius one and controlled from the whole external boundary. Namely, we consider the case of linear heat equations with lower order terms of order $0$ and $1$, and the case of a semilinear heat equations. In the linear case, we prove that any function which can be extended as an holomorphic function in a set of t…

A Holomorphic Splitting Theorem
Miao Song
https://arxiv.org/abs/2506.13517 https://arxiv.org/pdf/2506.13517

A Holomorphic Splitting Theorem
A long-term project is to construct a complete Calabi-Yau metric on the complement of the anticanonical divisor in a compact Kähler manifold $\oM$. We focus on the case where this smooth divisor has multiplicity 2 and is itself a compact Calabi-Yau manifold. Firstly we solved the Monge-Ampère equation when the Ricci potiential is of $O(r^{-1})$ decay on the generalized $ALG$ manifolds. Then we used the solution to this Kähler Ricci flat metric to prove a holomorphic splitting theorem: If $K_…

Holomorphic functions with Nash real part
Antonio Carbone
https://arxiv.org/abs/2507.17387 https://arxiv.org/pdf/2507.17387

Holomorphic functions with Nash real part
In this paper we show that a holomorphic function, defined on an open subset $D$ of $\mathbb{C}^n$, is a complex Nash function if and only if its real part (or equivalently its imaginary part) is a real Nash function.

On the connectedness of the singular set of holomorphic foliations
Omegar Calvo-Andrade, Maur\'icio Corr\^ea, Marcos Jardim, Jos\'e Seade
https://arxiv.org/abs/2506.08942 …

On the connectedness of the singular set of holomorphic foliations
Let $\mathcal{F}$ be a codimension 1 singular holomorphic foliation on $\mathbb{P}^3$ and let $Z$ be the union of the 1-dimensional connected components of its singular set; Dominique Cerveau asked in 2013 whether $Z$ is necessarily connected. We prove that if a $k$-dimensional holomorphic foliation on a projective manifold whose determinant bundle of the normal sheaf is ample has a singular set $Z$ of dimension $k-1$, then $Z$ is connected. This can be regarded as providing an obstruction for …

Quadratic Corrections to the Higher-Spin Equations by the Differential Homotopy Approach
P. T. Kirakosiants, D. A. Valerev, M. A. Vasiliev
https://arxiv.org/abs/2506.16634

Quadratic Corrections to the Higher-Spin Equations by the Differential Homotopy Approach
The recently proposed differential homotopy approach to the analysis of nonlinear higher spin theory is developed. The Ansatz is extended to the form applicable in the second order of the perturbation theory and general star-multiplication formulae are derived. The relation of the shifted homotopy and differential homotopy formalisms is worked out. Projectively-compact spin-local quadratic (anti)holomorphic vertices in the one-form sector of higher-spin equations are obtained within the differe…

An elementary proof of Newman's eta-quotient theorem
David Savitt
https://arxiv.org/abs/2507.16225 https://arxiv.org/pdf/2507.162…

An elementary proof of Newman's eta-quotient theorem
Let eta(z) be the Dedekind eta function. Newman studied the modularity of eta-quotients, giving necessary and sufficient conditions for a function of the form \prod_{0 < m | N} eta(mz)^{r_m} to be a (weakly) holomorphic modular form of level N. We explain a proof of Newman's theorem, developed while teaching a class for talented high school students at Canada/USA Mathcamp. The key observation is that although Gamma_1(N) is not generated by its upper triangular and lower triangular subgroup…

New results on universal Taylor series via weighted polynomial approximation
St\'ephane Charpentier (I2M), Konstantinos Maronikolakis
https://arxiv.org/abs/2506.20224

New results on universal Taylor series via weighted polynomial approximation
We use weighted polynomial approximation to prove the existence of a compact set K with non-empty interior and a function f is dense in the space A(K) of all continuous functions on K that are holomorphic in the interior of K, endowed with the sup norm, while the set This improves a result of Mouze. The main ideas of the proof also allows us to construct a holomorphic function while the modulus of its non-zero Taylor coecients go to $\infty$. In passing, we complement a result by Pritsker a…

Top Quark Bound States in Finite and Holomorphic Quantum Field Theories
E. J. Thompson
https://arxiv.org/abs/2507.16831 https://arxiv.org/pdf/2507.16831

Top Quark Bound States in Finite and Holomorphic Quantum Field Theories
We propose a unified theoretical study of the recently observed threshold enhancement in top-antitop production at the LHC known as toponium. First, we extend the finite, nonlocal quantum field theories to derive a modified Bethe-Salpeter equation for heavy quark-antiquark bound states, incorporating exp wential regulator functions that render all loop amplitudes ultraviolet finite. We show that nonlocal propagators induce characteristic shifts in the resonance mass and width, which can be cont…

Local classification of K\"ahler metrics with constant holomorphic sectional curvature
Martin de Borbon
https://arxiv.org/abs/2507.06855 https://

Local classification of Kähler metrics with constant holomorphic sectional curvature
We prove the local classification of Kähler metrics with constant holomorphic sectional curvature by exploiting the geometry of the bundle of 1-jets of holomorphic functions.

Rigidity of proper holomorphic self-mappings of the hexablock
Enchao Bi, Zeinab Shaaban, Guicong Su
https://arxiv.org/abs/2507.16176 https://

Rigidity of proper holomorphic self-mappings of the hexablock
The hexablock \(\mathbb{H}\), introduced by Biswas-Pal-Tomar \cite{Hexablock}, is a Hartogs domain in \(\mathbb{C}^4\) fibered over the tetrablock \(\mathbb{E}\) in \(\mathbb{C}^3\), arising in the context of \(μ\)-synthesis problems. In this paper, we prove that every proper holomorphic self-map of \(\mathbb{H}\) is necessarily an automorphism. Consequently, we resolve the conjecture \(G(\mathbb{H}) = \mathrm{Aut}(\mathbb{H})\) on the automorphism group structure, originally posed by Biswas-P…

Holomorphic bootstrap for RCFT: signs and bounds for quasi-characters
Arpit Das, Sunil Mukhi
https://arxiv.org/abs/2507.07170 https://

Holomorphic bootstrap for RCFT: signs and bounds for quasi-characters
Quasi-characters are solutions of simple modular differential equations that form an explicit basis for the space of all admissible characters that can potentially describe rational CFT. They were classified for rank-$2$ in arXiv:1810.09472 [hep-th], where it was conjectured that their $q$-series has coefficients of alternating sign that stabilise to a fixed sign at order $\frac{c}{12}$ and sometimes undergo more exotic behaviour -- where $c$ is the central charge. Here we prove some of these c…

Spectral bundles on Abelian varieties, complex projective spaces and Grassmannians
Ching-Hao Chang, Jih-Hsin Cheng, I-Hsun Tsai
https://arxiv.org/abs/2507.14458

Spectral bundles on Abelian varieties, complex projective spaces and Grassmannians
In this paper we study the spectral analysis of Bochner-Kodaira Laplacians on an Abelian variety, complex projective space $\mathbb{P}^{n}$ and a Grassmannian with a holomorphic line bundle. By imitating the method of creation and annihilation operators in physics, we convert those eigensections (of the \textquotedblleft higher energy" level) into holomorphic sections (of the \textquotedblleft lowest energy" level). This enables us to endow these spectral bundles, which are defined over the dua…

A monomial basis for the holomorphic functions on certain Banach spaces
Thiago Grando, Mary Lilian Louren\c{c}o
https://arxiv.org/abs/2507.05138 https://…

A monomial basis for the holomorphic functions on certain Banach spaces
In this article, we prove that the monomials form a basis for the space of holomorphic functions $(\mathcal{H}(Z), τ_0)$, where $Z$ denotes either the space $c_0\left(\bigoplus^\infty_{i=1}\ell^i_p \right)$ for some $p\in [1, \infty)$, or the space $d_*(w,1)$, which is the predual of the Lorentz sequence space $d(w,1)$. To achieve this, we first define a fundamental system of compact subsets in $Z$, and, based on this characterization, construct a family of seminorms that generate the topology…

Towards a general distortion theory for univalent functions: Teichmuller spaces and coefficient problems of complex analysis
Samuel L. Krushkal
https://arxiv.org/abs/2507.19767 …

Towards a general distortion theory for univalent functions: Teichmuller spaces and coefficient problems of complex analysis
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental intrinsic features of holomorphy and of conformality. This paper surveys the results obtained by a new approach involving deep features of Teichmuller spaces. This approach was recently suggested by the author. The paper also contains some new results genera…

Real Bialynicki-Birula flows in moduli spaces of Higgs bundles
Florent Schaffhauser, Tommaso Scognamiglio
https://arxiv.org/abs/2507.18613 https://arxiv.or…

Real Bialynicki-Birula flows in moduli spaces of Higgs bundles
Let $X$ be a compact Riemann surface $X$ of genus $\geqslant 2$ and let $σ:X \to X$ be an anti-holomorphic involution. Using real and quaternionic systems of Hodge bundles, we study the topology of the real locus $\mathbb{R} \mathbf{M}_{\mathrm{Dol}}(r,d)$ of the moduli space of semistable Higgs bundles of rank $r$ and degree $d$ on $X$, for the induced real structure $(E,ϕ) \to (σ^*(\overline{E}),σ^*(\overlineϕ))$. We show in particular that, when $\mathrm{gcd}(r,d)=1$, the number of conn…

Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators
Jorge J. Betancor, Estefan\'ia Dalmasso, Pablo Quijano
https://arxiv.org/abs/2506.14631

Variational inequalities associated with the semigroups generated by fractional Kolmogorov operators
In this paper we consider fractional Kolmogorov operators defined, in $\mathbb{R}^d$, by \[Λ_κ=(-Δ)^{α/2}+\fracκ{|x|^α} x\cdot \nabla,\] with $α\in (1,2)$, $α<(d+2)/2$ and $κ\in \mathbb{R}$. The operator $Λ_α$ generates a holomorphic semigroup $\{T_t^α\}_{t>0}$ in $L^2(\mathbb{R}^d)$ provided that $κ<κ_c$ where $κ_c$ is a critical coupling constant. We establish $L^p$-boundedness properties for the variation operators $V_ρ\left(\{t^\ell\partial_t^\ell T_t^α\}_{t>0…

This https://arxiv.org/abs/2412.18095 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Zee model in a non-holomorphic modular $A_4$ symmetry
We study a Zee model in a non-holomorphic modular $A_4$ flavor symmetry in which we find good predictions in both the cases of normal and inverted hierarchy. Parameter reduction on neutrino sector occurs due to large mass hierarchies between charged-leptons mass eigenvalues and new singly-charged bosons in addition to this flavor symmetry. As a result, we have two complex free parameters including modulus $τ$. We show several predictions in terms of verifiable observables such as Dirac CP, Maj…

A Burns-Krantz type theorem for Blaschke products
Annika Moucha
https://arxiv.org/abs/2505.21346 https://arxiv.org/pdf/2505.21346

A Burns-Krantz type theorem for Blaschke products
Let $f$ be a holomorphic function mapping the open unit disk into itself. We establish a boundary version of Schwarz' lemma in the spirit of a result by Burns and Krantz and provide sufficient conditions on the local behaviour of $f$ near some boundary point that forces $f$ to be a Blaschke product with predescribed critical points. For the proof, a local Julia type inequality based on Nehari's sharpening of Schwarz' lemma is established.

On the geometry of holomorphic curves and complex surface
Amanda Dias Falqueto, Farid Tari
https://arxiv.org/abs/2505.24719 https://a…

On the geometry of holomorphic curves and complex surface
We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that measure the contact between curves or surfaces and model objects become holomorphic. This allows the application of singularity theory, yielding analogues of classical results from the real case. Our approach enables the definition of geometric invariants of curves…

The cohomological Kudla conjecture for unitary Shimura varieties
Fran\c{c}ois Greer, Salim Tayou
https://arxiv.org/abs/2507.13299 https://

The cohomological Kudla conjecture for unitary Shimura varieties
We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature $(n+1,1)$ and prove that they are holomorphic Hermitian modular forms. This proves the cohomological version of a conjecture of Kudla and Bruinier--Rosu--Zemel, in all codimensions up to the middle. We also develop the theory of Hermitian quasi-modular forms, with a particular focus on polynomial weighted theta functions, and prov…

On the relation between distances and seminorms on Fr\'echet spaces, with application to isometries
Isabelle Chalendar, Lucas Oger, Jonathan R. Partington
https://arxiv.org/abs/2506.16801

On the relation between distances and seminorms on Fréchet spaces, with application to isometries
A study is made of linear isometries on Fréchet spaces for which the metric is given in terms of a sequence of seminorms. This establishes sufficient conditions on the growth of the function that defines the metric in terms of the seminorms to ensure that a linear operator preserving the metric also preserves each of these seminorms. As an application, characterizations are given of the isometries on various spaces including those of holomorphic functions on complex domains and continuous func…

Torsors over moduli spaces of vector bundles over curves of fixed determinant
Indranil Biswas, Jacques Hurtubise
https://arxiv.org/abs/2507.05690 https://

Torsors over moduli spaces of vector bundles over curves of fixed determinant
Let ${\mathcal M}$ be a moduli space of stable vector bundles of rank $r$ and determinant $ξ$ on a compact Riemann surface $X$. Fix a semistable holomorphic vector bundle $F$ on $X$ such that $χ(E\otimes F)= 0$ for $E \in \mathcal M$. Then any $E\in \mathcal M$ with $H^0(X, E\otimes F) = 0 = H^1(X, E\otimes F)$ has a natural holomorphic projective connection. The moduli space of pairs $(E,\, \nabla)$, where $E\, \in\, \mathcal M$ and $\nabla$ is a holomorphic projective connection on $E$, is …

Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
Hank Chen, Joaquin Liniado
https://arxiv.org/abs/2507.01858 https://

Infinite Dimensional Topological-Holomorphic Symmetry in Three-Dimensions
We introduce a three-dimensional quantum field theory with an infinite-dimensional symmetry, realized explicitly through a centrally extended affine graded Lie algebra. This symmetry is a direct three-dimensional generalization of the chiral symmetry in the Wess-Zumino-Witten model. Accordingly, this setup provides a framework for extending the methods of two-dimensional conformal field theory to three dimensions, and we expect it to lay the groundwork for exact methods in three-dimensional qua…

This https://arxiv.org/abs/2504.19731 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tian's theorem for Grassmannian embeddings and degeneracy sets of random sections
Let $(X,ω)$ be a compact Kähler manifold, $(L,h^L)$ be a positive line bundle, and $(E,h^E)$ be a Hermitian holomorphic vector bundle of rank $r$ on $X$. We prove that the pullback by the Kodaira embedding associated to $L^p\otimes E$ of the $k$-th Chern class of the dual of the universal bundle over the Grassmannian converges as $p\to\infty$ to the $k$-th power of the Chern form $c_1(L,h^L)$, for $0\leq k\leq r$. If $c_1(L,h^L)=ω$ we also determine the second term in the semiclassical expan…

Averaging quadratically twisted $L$-values and their derivatives
Tinghao Huang
https://arxiv.org/abs/2507.00179 https://arxiv.org/pdf…

Averaging quadratically twisted $L$-values and their derivatives
In this paper, we unconditionally establish an asymptotic formula for the product of the quadratically twisted central $L$-value associated to a holomorphic cusp form $f$, and the quadratically twisted central $L$-derivative to a distinct holomorphic cusp form $g$. This result may be viewed as an extension of \cite{Li-MR4768632}, \cite{Kumar.etc-MR4765788} and \cite{zhou2025momentderivativesquadratictwists}.

This https://arxiv.org/abs/2410.07655 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sobolev and Hölder estimates for the $\overline \partial$ equation on pseudoconvex domains of finite type in $\mathbb C^2$
We prove a homotopy formula which yields almost sharp estimates in all (positive-indexed) Sobolev and Hölder-Zygmund spaces for the $\overline \partial$ equation on pseudoconvex domains of finite type in $\mathbb C^2$, extending the earlier results of Fefferman-Kohn (1988), Range (1990), and Chang-Nagel-Stein (1992). The main novelty of our proof is the construction of holomorphic support functions that admit precise estimates when the parameter variable lies in a thin shell outside the domain.

Lines in the space of K\"ahler metrics
Tam\'as Darvas, Nicholas McCleerey
https://arxiv.org/abs/2507.17375 https://arxiv.org/pdf/2507.17375…

Lines in the space of Kähler metrics
We establish a Ross-Witt Nyström correspondence for weak geodesic lines in the (completed) space of Kähler metrics. We construct a wide range of weak geodesic lines on arbitrary projective Kähler manifolds that are not generated by holomorphic vector fields, thus disproving a folklore conjecture popularized by Berndtsson. Remarkably, some of these weak geodesic lines turn out to be smooth. In the case of Riemann surfaces, our results can be significantly sharpened. Finally, we investigate th…

Moduli of Higgs Coherent Systems with stable underlying vector bundles over a curve
Casta\~neda-Gonz\'alez Edgar I
https://arxiv.org/abs/2507.15161 htt…

Moduli of Higgs Coherent Systems with stable underlying vector bundles over a curve
Let $X$ be a smooth, connected complex projective curve of genus at least $2$. A Higgs coherent system is an augmented bundle $(E,V)$, where $E$ is a holomorphic vector bundle, and $V$ is a linear subspace of the spaces of Higgs bundles of $E$. The purpose of this paper is twofold. First, we introduce the moduli problem of Higgs coherent systems over $X$. Second, we construct the fine moduli space for Higgs coherent systems with stable underlying vector bundles.

Sphericity and Analyticity of a strictly pdeusoconvex hypersurface in low regularity I
Ilya Kossovskiy, Dmitri Zaitsev
https://arxiv.org/abs/2506.20177 htt…

Sphericity and Analyticity of a strictly pdeusoconvex hypersurface in low regularity I
In our earlier work \cite{KZ}, we introduced an analytic regularizability theory for smooth strictly pseudoconvex hypersurfaces in complex space. That is, we found a necessary and sufficient condition for a hypersurface to be CR-equivalent to an analytic target. The condition amount to the holomorphic extension property for a smooth function on a totally real submanifold, both the function and the submanifold being uniquely associated with the given hypersurface. In the present paper, we deve…

On the Effective Non-vanishing of Rankin--Selberg $L$-functions at Special Points
Zhi Qi
https://arxiv.org/abs/2506.08546 https://arx…

On the Effective Non-vanishing of Rankin--Selberg $L$-functions at Special Points
Let $Q (z)$ be a holomorphic Hecke cusp newform of square-free level and $u_j (z)$ traverse an orthonormal basis of Hecke--Maass cusp forms of full level. Let $1/4 + t_j^2$ be the Laplace eigenvalue $u_j (z)$. In this paper, we prove that there is a constant $ γ(Q) $ expressed as a certain Euler product associated to $Q$ such that at least $ γ(Q) / 11 $ of the Rankin--Selberg special $L$-values $L (1/2+it_j, Q \otimes u_j)$ for $ t_j \leqslant T$ do not vanish as $T \rightarrow \infty$. Furth…

Multi-centered Black Hole Quantum Mechanics and Generalized Error Functions
Boris Pioline, Rishi Raj
https://arxiv.org/abs/2507.08551 https://

Multi-centered Black Hole Quantum Mechanics and Generalized Error Functions
In type II Calabi-Yau string compactifications, S-duality predicts that suitable generating series of BPS indices counting micro-states of D4-D2-D0 black holes are in general mock modular forms of higher depth. The non-holomorphic contributions needed to cancel the anomaly under modular transformations involve certain indefinite theta series with kernels constructed from generalized error functions. Physically, these contributions are expected to arise from a spectral asymmetry in the continuum…

Scattering theory on Riemann surfaces I: Schiffer operators, cohomology, and index theorems
Eric Schippers, Wolfgang Staubach
https://arxiv.org/abs/2506.08160

Scattering theory on Riemann surfaces I: Schiffer operators, cohomology, and index theorems
We consider a compact Riemann surface $\mathscr{R}$ with a complex of non-intersecting Jordan curves, whose complement is a pair of Riemann surfaces with boundary, each of which may be possibly disconnected. We investigate conformally invariant integral operators of Schiffer, which act on $L^{2}$ anti-holomorphic one-forms on one of these surfaces with boundary and produce holomorphic one-forms on the disjoint union. These operators arise in potential theory, boundary value problems, approximat…

Intersection numbers between horizontal foliations of quadratic differentials
Dragomir Saric, Taro Shima
https://arxiv.org/abs/2506.14943 https://

Intersection numbers between horizontal foliations of quadratic differentials
We establish that the intersection number between the horizontal foliations of any two finite-area holomorphic quadratic differentials on an arbitrary Riemann surface is finite. Our main result shows that the intersection number is jointly continuous in the $L^1$-norm on the quadratic differentials. A corollary is that the Jenkins-Strebel differentials are not dense in the space of all finite-area holomorphic quadratic differentials when the infinite Riemann surface is not parabolic.

Replaced article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- Holomorphic Koszul-Brylinski homologies of Poisson blow-ups
Xiaojun Chen, Youming Chen, Song Yang, Xiangdong Yang

Unlocking the Hodge Conjecture: A Spectral Fingerprint Approach via Gauss-Manin Derivatives
Bita Hajebi, Pooya Hajebi
https://arxiv.org/abs/2507.13064 http…

Unlocking the Hodge Conjecture: A Spectral Fingerprint Approach via Gauss-Manin Derivatives
We present a symbolic analytic framework for addressing the Hodge Conjecture, based on a refined invariant called the Hermitian spectral fingerprint. By projecting out $(k,k)$ components from holomorphic forms and their Gauss Manin derivatives, we define a fingerprint functional that vanishes identically for any rational cohomology class of type $(k,k)$. We prove unconditionally that the projected derivatives span the entire orthogonal complement of $H^{k,k}(X)$ in $H^{2k}(X,\mathbb{C})$, imply…

Cusp forms as $p$-adic limits circumventing $p$-adic version of the Legendre period relation
Pavel Guerzhoy
https://arxiv.org/abs/2506.07107 https://

Cusp forms as $p$-adic limits circumventing $p$-adic version of the Legendre period relation
Several authors have recently proved results which express a cusp form as a $p$-adic limit of weakly holomorphic modular forms under repeated application of Atkin's $U$-operator. Initially, these results had a deficiency: one could not rule out the possibility when a certain quantity vanishes and the final result fails to be true. Later on, Ahlgren and Samart \cite{AS} found a method to prove that no exceptions happen in the specific case considered by El-Guindy and Ono, Hanson and Jameson, and…

Characterization of negative line bundles whose Grauert blow-down are quadratic transforms
Fusheng Deng, Yinji Li, Qunhuan Liu, Xiangyu Zhou
https://arxiv.org/abs/2506.14264

Characterization of negative line bundles whose Grauert blow-down are quadratic transforms
We show that the Grauert blow-down of a holomorphic negative line bundle $L$ over a compact complex space is a quadratic transform if and only if $k_0L^*$ is very ample and $(k_0+1)L^*$ is globally generated, where $k_0$ is the initial order of $L^*$, namely, the minimal integer such that $k_0^*$ has nontrivial holomorphic section.

Nakano-Griffiths inequality, holomorphic Morse inequalities, and extension theorems for $q$-concave domains
Bingxiao Liu, George Marinescu, Huan Wang
https://arxiv.org/abs/2506.00879

Nakano-Griffiths inequality, holomorphic Morse inequalities, and extension theorems for $q$-concave domains
We consider a compact $n$-dimensional complex manifold endowed with a holomorphic line bundle that is semi-positive everywhere and positive at least at one point. Additionally, we have a smooth domain of this manifold whose Levi form has at least $n-q$ negative eigenvalues ($1\leq q\leq n-1$) on the boundary. We prove that every $\overline{\partial}_b$-closed $(0,\ell)$-form on the boundary with values in a holomorphic vector bundle admits a meromorphic extension for all $q\leq \ell\leq n-1$. T…

Minimal tori in $\mathbb{R}^4$
Marc Soret, Marina Ville
https://arxiv.org/abs/2507.12914 https://arxiv.org/pdf/2507.12914

Minimal tori in $\mathbb{R}^4$
We describe tools for the study of minimal surfaces in $\mathbb{R}^4$; some are classical (the Gauss maps) and some are newer (the link/braid/writhe at infinity). Then we look for complete proper non holomorphic minimal tori with total curvature $-8π$ and a single end immersed in $\mathbb{R}^4$. We translate the problem into a system of $10$ quadratic or linear equations in $11$ real variables with coefficients in terms of the Weierstrass function $\wp$ and give explicit solutions for these eq…

A Quaternionic Integration Similar to the Complex One
Michael Parfenov
https://arxiv.org/abs/2506.16239 https://arxiv.org/pdf/2506.16…

A Quaternionic Integration Similar to the Complex One
The conception of C- and H-representations of any holomorphic function is further extended to the notions, definitions, lemmas and theorems of the complex integration. On this basis and the introduced notion of a H-plane, generalising the notion of a number complex plane, the theory of the quaternionic integration similar to the complex one is built. The complex Taylor Theorem, Cauchy's Theorem, Cauchy's Integral Formula, Laurent's series, Laurent's theorem, and Cauchy's Residue Theorem are dir…

Complex harmonic maps and rank 2 higher Teichm\"uller theory
Christian El Emam, Nathaniel Sagman
https://arxiv.org/abs/2506.11746 https://

Complex harmonic maps and rank 2 higher Teichmüller theory
We initiate and develop the theory of complex harmonic maps to holomorphic Riemannian symmetric spaces, which we make use of to study complex analytic aspects of higher Teichmüller theory, with a focus on rank $2$ Hitchin components. Complex harmonic maps lead to various generalizations of objects from the theory of Higgs bundles; for instance, the Hitchin fibration, cyclic Higgs bundles, and the affine Toda equations. Beyond such generalizations, we also find a relation between complex harm…

Remarks on Higgs bundles twisted by a vector bundle
David Alfaya, Indranil Biswas, Pradip Kumar
https://arxiv.org/abs/2506.06573 https://

Remarks on Higgs bundles twisted by a vector bundle
For any V-twisted Higgs bundle on a compact Riemann surface X, where V is a holomorphic vector bundle of rank two on X, there are two associated Higgs bundles on X, twisted by line bundles, which are constructed using a Hecke transformation on V. We characterize all such pairs of Higgs bundles (twisted by line bundles) given by V-twisted Higgs bundles. Using this characterization, we provide a spectral correspondence for the moduli space, identifying V-twisted Higgs bundles with the direct imag…

$p$-adic moments of $L$-functions
Daniel Kriz, Asbj{\o}rn Christian Nordentoft
https://arxiv.org/abs/2507.01836 https://arxiv.org/pdf…

$p$-adic moments of $L$-functions
We obtain a formula for the $p$-adic valuation of weighted moments of central $L$-values of holomorphic cusp forms twisted by Dirichlet characters of order $p$. In some cases we give an arithmetic interpretation of the constants in the formula. The result is obtained via the study of the digit map, turning a horizontal $p$-adic measure into a vertical one, applied to the horizontal $p$-adic $L$-functions as defined by the authors in previous work.

Perturbations of Vector Bundle whose Curvature Form Solves a Polynomial Equation
R\'emi Delloque
https://arxiv.org/abs/2507.01534 https://

Perturbations of Vector Bundle whose Curvature Form Solves a Polynomial Equation
We investigate the behaviour of local perturbations of a wide class of geometric PDEs on holomorphic Hermitian vector bundles over a compact complex manifold. Our main goal is to study the existence of solutions near an initial solution under small deformations of both the holomorphic structure of the bundle and the parameters of the equation. Inspired by techniques from geometric invariant theory and the moment map framework, under suitable assumptions on the initial solution, we establish a l…

This https://arxiv.org/abs/2505.13114 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Kahlerian approche to the Schrodinger equation in Siegel jacobi Space of the lognormal distribution
In this paper, we describe the evolution of spectral curves in the Siegel Jacobi space through the Schrodinger equation constructed from a Kahler geometry induced on the lognormal statistical manifold via Dombrowski's construction. We introduce new holomorphic structures and show that the Hamiltonian vector field coincides with the fundamental vector field generated by holomorphic isometries. We construct the time dependent Schrodinger equation from this geometric setting and show that the asso…

Toric reduction of singularities for Newton non-degenerate $p$-forms
Bilal Balo
https://arxiv.org/abs/2507.05430 https://arxiv.org/pd…

Toric reduction of singularities for Newton non-degenerate $p$-forms
We study a class of holomorphic $p$-forms satisfying non-degeneracy conditions expressed through their Newton polyhedron. We show that a regular refinement of their dual fan defines a toric reduction of singularities to a log-smooth $p$-form.

Carath\'eodory distance-preserving maps between bounded symmetric domains
Bas Lemmens, Cormac Walsh
https://arxiv.org/abs/2507.08639 https://

Carathéodory distance-preserving maps between bounded symmetric domains
We study the rigidity of maps between bounded symmetric domains that preserve the Carathéodory/Kobayashi distance. We show that such maps are only possible when the rank of the co-domain is at least as great as that of the domain. When the ranks are equal, and the domain is irreducible, we prove that the map is either holomorphic or antiholomorphic. In the holomorphic case, we show that the map is in fact a triple homomorphism, under the additional assumption that the origin is mapped to the o…

This https://arxiv.org/abs/2505.00799 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quantum Modular Forms and Resurgence
In 2010, Zagier described a new phenomenon which he called quantum modularity. This connected various examples coming from disparate fields which exhibit near-modular behavior. In the fifteen years since, Zagier's philosophy has informed new developments in areas such as knot theory, 3-dimensional topology, combinatorics, and physics. More recently, the concept of holomorphic quantum modularity has emerged, pointing to a clearer structure for Zagier's original examples. These new developments s…

Decay of Fourier transforms and analytic continuation of power-constructible functions
Georges Comte, Dan J. Miller, Tamara Servi
https://arxiv.org/abs/2507.06142

Decay of Fourier transforms and analytic continuation of power-constructible functions
For a subfield K of C, we denote by C^K the category of algebras of functions defined on the globally subanalytic sets that are generated by all K-powers and logarithms of positively-valued globally subanalytic functions. For any function f in C^\K(R), we study links between holomorphic extensions of f and the decay of its Fourier transform F[f] by using tameness properties of the globally subanalytic functions from which f is constructed. We first prove a number of theorems about analytic cont…

Bicomplex Hardy Classes of Solutions to Beltrami Equations and the Schwarz Boundary Value Problem
William L. Blair
https://arxiv.org/abs/2507.15657 https:/…

Bicomplex Hardy Classes of Solutions to Beltrami Equations and the Schwarz Boundary Value Problem
We define Hardy classes of bicomplex-valued functions on the complex unit disk which solve bicomplex versions of the Beltrami and related equations. Using representations in terms of their complex-valued counterparts, we show these bicomplex-valued functions recover the boundary behavior associated with the classic holomorphic Hardy spaces. This work generalizes known results for complex-valued functions and continues recent work in the setting of bicomplex analogues of Hardy spaces of both hol…

Segre forms of singular metrics on vector bundles and Lelong numbers
Mats Andersson, Richard L\"ark\"ang
https://arxiv.org/abs/2506.15473 https:/…

Segre forms of singular metrics on vector bundles and Lelong numbers
Let $E\to X$ be a holomorphic vector bundle with a singular Griffiths negative Hermitian metric $h$ with analytic singularities. One can define, given a smooth reference metric $h_0$, a current $s(E,h,h_0)$ that is called the associated Segre form, which defines the expected Bott-Chern class and coincides with the usual Segre form of $h$ where it is smooth. We prove that $s(E,h,h_0)$ is the limit of the Segre forms of a sequence of smooth metrics if the metric is smooth outside the unbounded lo…

Bubbling of rank two bundles over surfaces
Xuemiao Chen
https://arxiv.org/abs/2506.09614 https://arxiv.org/pdf/2506.09614

Bubbling of rank two bundles over surfaces
In this paper, motivated by the singularity formation of ASD connections in gauge theory, we study an algebraic analogue of the singularity formation of families of rank two holomorphic vector bundles over surfaces. For this, we define a notion of fertile families bearing bubbles and give a characterization of it using the related discriminant. Then we study families that locally form the singularity of the type $\mathcal{O}\oplus \mathcal{I}$ where $\mathcal{I}$ is an ideal sheaf defining poin…

On the equivariant vector bundles on $\mathbb{CP}^1$
Indranil Biswas, Manish Kumar, A. J. Parameswaran
https://arxiv.org/abs/2507.02359 https://

On the equivariant vector bundles on $\mathbb{CP}^1$
Let $H$ be a subgroup of ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) such that the Zariski closure in ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) of some compact subgroup of $H$ contains $H$. We classify the $H$--equivariant holomorphic vector bundles on $\mathbb{CP}^1$. This generalizes \cite{BM} where $H$ was assumed to be a finite abelian group.

Schauder Basis With Finite Blaschke Products
E Fricain (LPP), J Mashreghi (ULaval), M Nasri (LPP), M Ostermann (LPP)
https://arxiv.org/abs/2507.13121 https…

Schauder Basis With Finite Blaschke Products
We construct a Schauder basis for the space $Hol(\mathbb D)$, the space of holomorphic functions on the closed unit disk, consisting entirely of finite Blaschke products. The expansion coefficients are given explicitly. Our result remains valid when $Hol(\mathbb D)$ is equipped with a broader class of norms satisfying natural structural conditions. These conditions are satisfied by norms of classical function spaces such as the Hardy spaces $H^p$ ($1\leq p\leq \infty$), the weighted Bergman spa…

$L^2$-Hodge theory of Hybrid Landau-Ginzburg models of Calabi-Yau complete intersections
Jeehoon Park, Jaewon Yoo
https://arxiv.org/abs/2505.24218 https://…

$L^2$-Hodge theory of Hybrid Landau-Ginzburg models of Calabi-Yau complete intersections
Given a Calabi-Yau smooth projective complete intersection variety $V$ over $\C$, a hybrid Landau-Ginzburg (LG) model may be associated using the Cayley trick. This hybrid LG model comprises a non-compact Calabi-Yau manifold $X_{CY}$, and a holomorphic function $W$, defined on $X_{CY}$, such that the critical locus of $W$ is isomorphic to $V$. We construct a complete Kähler metric $\mathfrak{g}$ and a bounded Calabi-Yau volume form $Ω$ on $X_{CY}$ such that $(X_{CY},\mathfrak{g}, Ω)$ is a bo…

Replaced article(s) found for math.CV. https://arxiv.org/list/math.CV/new
[1/1]:
Holomorphic automorphisms of Markov-type surfaces
https://

Monogenic functions over real alternative *-algebras: the several hypercomplex variables case
Zhenghua Xu, Chao Ding, Haiyan Wang
https://arxiv.org/abs/2506.08307

Monogenic functions over real alternative *-algebras: the several hypercomplex variables case
The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of monogenic functions over real alternative $\ast$-algebras has been introduced to unify several classical monogenic functions theories. In this paper, we initiate the study of monogenic functions of several hypercomplex variables over real alternative $\ast$-al…

Geometric effects of hyperbolic cohomology classes on K\"ahler manifolds
Francesco Bei, Simone Diverio, Stefano Trapani
https://arxiv.org/abs/2506.09907

Geometric effects of hyperbolic cohomology classes on Kähler manifolds
We introduce the notion of Kähler topologically hyperbolic manifold, as a"topological" generalization of Kähler [Gro91] and weakly Kähler [BDET24] hyperbolic manifolds. Analogously to [BCDT24], we show the birational invariance of this property and then that Kähler topologically hyperbolic manifolds are not uniruled nor bimeromorphic to compact Kähler manifolds with trivial first real Chern class. Then, we prove spectral gap theorems for positive holomorphic Hermitian vector bundles on Kä…