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Contact loci of semihomogeneous singularities
Eduardo de Lorenzo Poza, Jiahui Huang
https://arxiv.org/abs/2506.18805 https://arxiv.or…

Contact loci of semihomogeneous singularities
Two of the main open problems in the theory of contact loci are the arc-Floer conjecture, which states that the compactly supported cohomology of the restricted $m$-contact locus and the fixed-point Floer cohomology of the $m$-th iterate of the Milnor monodromy are isomorphic up to a shift; and the embedded Nash problem, which asks for a description of the irreducible components of the unrestricted $m$-contact locus in terms of an embedded resolution of singularities. In this paper we study the…

Replaced article(s) found for physics.bio-ph. https://arxiv.org/list/physics.bio-ph/new
[1/1]:
- Static Three-Dimensional Structures Determine Fast Dynamics Between Distal Loci Pairs in Interpha...
Guang Shi, Sucheol Shin, D. Thirumalai

Proper Fourier-Mukai partners of abelian varieties and points outside the Fourier-Mukai loci in Matsui spectra
Hisato Matsukawa
https://arxiv.org/abs/2506.13527

Proper Fourier-Mukai partners of abelian varieties and points outside the Fourier-Mukai loci in Matsui spectra
We prove that any smooth proper Fourier-Mukai partner of an abelian variety is an abelian variety by computing the Matsui spectrum of the derived category. While this result was previously shown by Huybrechts and Nieper-Wisskirchen in the case of smooth projective varieties, we extended it to the proper setting using a completely different method. We also show that, for certain proper schemes, the set of points lying outside the Fourier-Mukai locus in the Matsui spectrum of the derived catego…

This https://arxiv.org/abs/2411.00957 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Modularity of $d$-elliptic loci with level structure
We consider the generating series of special cycles on $\mathcal{A}_1(N)\times \mathcal{A}_g(N)$, with full level $N$ structure, valued in the cohomology of degree $2g$. The modularity theorem of Kudla-Millson for locally symmetric spaces implies that these series are modular. When $N=1$, the images of these loci in $\mathcal{A}_g$ are the $d$-elliptic Noether-Lefschetz loci, which are conjectured to be modular. In the appendix, it is shown that the resulting modular forms are nonzero for $g=2$…

Soft theorems of tree-level ${\rm Tr}(\phi^3)$, YM and NLSM amplitudes from $2$-splits
Kang Zhou
https://arxiv.org/abs/2506.00747 https://

Soft theorems of tree-level ${\rm Tr}(ϕ^3)$, YM and NLSM amplitudes from $2$-splits
In this paper, we extend the method proposed in \cite{Arkani-Hamed:2024fyd} for deriving soft theorems of amplitudes, which relies exclusively on factorization properties including conventional factorizations on physical poles, as well as newly discovered $2$-splits on special loci in kinematic space. Using the extended approach, we fully reproduce the leading and sub-leading single-soft theorems for tree-level ${\rm Tr}(ϕ^3)$ and Yang-Mills (YM) amplitudes, along with the leading and sub-lead…

Real Toric Varieties: Interactions between their Geometry and their Topology
Jules Chenal (LPP), Matilde Manzaroli
https://arxiv.org/abs/2506.03745 https:/…

Real Toric Varieties: Interactions between their Geometry and their Topology
In the present article, we investigate the topology of real toric varieties, especially those whose torus is not split over the field of real numbers. We describe some canonical fibrations associated to their real loci. Then, we establish various properties of their cohomology provided that their real loci are compact and smooth. For instance, we compute their Betti numbers, show that their cohomology is totally algebraic, and extend a criterion of orientability. In addition, we provide the top…

Quasi-Homogeneous Integrable Systems: Free Parameters, Kovalevskaya Exponents, and the Painlev\'e Property
Changyu Zhou, Hayato Chiba
https://arxiv.org/abs/2505.24330

Quasi-Homogeneous Integrable Systems: Free Parameters, Kovalevskaya Exponents, and the Painlevé Property
This paper investigates quasi-homogeneous integrable systems by analyzing their Laurent series solutions near movable singularities, motivated by patterns observed in Kovalevskaya exponents of four-dimensional Painlevé-type equations. We introduce a parameter space encoding the free coefficients in these expansions and study its deformation under a commuting quasi-homogeneous vector field. Within this framework, we derive lower indicial loci from the principal one and establish an arithmetic…

On the Virtual Euler Characteristic of the Moduli Space of Stable Pairs on Surfaces
Ana Pavlakovi\'c
https://arxiv.org/abs/2505.23531 https://

On the Virtual Euler Characteristic of the Moduli Space of Stable Pairs on Surfaces
We study the stable pair theory on toric surfaces and determine the virtual tangent space over the fixed point loci. Further, we present a program to compute the virtual Euler characteristic, illustrated by the case of the projective plane. As an application, conjectures regarding rationality and symmetry are supported by verification of a special case.