Tootfinder

This https://arxiv.org/abs/2401.10771 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Study of Orbital Dynamics in Singular and Regular Naked Singularity Space-times
The universe is filled with various compact objects and the most attractive of them are the black holes and singularity. But it is also known that at the singularity density becomes so infinitely high that the present physics knowledge breaks down. Thus, the singularity remains a flaw of the present theories. Several methods have been exercised to resolve the singularity. One such mathematical method is through conformal transformations. This paper deals with regularizing a naked singularity sp…

This https://arxiv.org/abs/2401.10771 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Study of Orbital Dynamics in Singular and Regular Naked Singularity Space-times
The universe is filled with various compact objects and the most attractive of them are the black holes and singularity. But it is also known that at the singularity density becomes so infinitely high that the present physics knowledge breaks down. Thus, the singularity remains a flaw of the present theories. Several methods have been exercised to resolve the singularity. One such mathematical method is through conformal transformations. This paper deals with regularizing a naked singularity sp…

Mutual singularity of Riesz products on the unit sphere
Evgueni Doubtsov
https://arxiv.org/abs/2404.02652 https://arxiv.org/pdf/2404.…

Mutual singularity of Riesz products on the unit sphere
We prove analogs of Peyrière's mutual singularity theorem for standard and generalized Riesz products on the unit sphere of $\mathbb{C}^n$, $n\ge 2$. As a corollary, we obtain an analog of Zygmund's dichotomy for the Riesz products under consideration.

The Social Media Sameness Singularity (Smith, 2016) continues.
https://www.theverge.com/2024/4/3/24119721/facebook-updated-full-screen-video-player-vertical-view

Facebook’s new full-screen video player looks a lot like TikTok
The platform’s update will feature vertical videos by default, bringing the full-screen, vertically oriented look to Reels, Facebook Live, and longform videos.

On coincidences of singular loci of types $\Sigma^{1_r}$ and $\Sigma^r$
Andr\'as Cs\'epai, Andr\'as Sz\H{u}cs, Tam\'as Terpai
https://arxiv.org/abs/2403.00332

On coincidences of singular loci of types $Σ^{1_r}$ and $Σ^r$
It is well-known that the Thom polynomial in Stiefel--Whitney classes expressing the cohomology class dual to the locus of the cusp singularity for codimension-$k$ maps $Σ^{1_2}(k)$ and that of the corank-$2$ singularity for codimension-$(k-1)$ maps $Σ^2(k-1)$ coincide: both are $w_{k+1}^2 + w_k w_{k+2}$. The aim of the present paper is to find out whether there is any geometric explanation to this seemingly mysterious coincidence. We thank László Fehér for posing us this interesting quest…

Oscillatory free boundary problems in stochastic materials
Dami\~ao J. Ara\'ujo, Ginaldo S. S\'a, Eduardo V. Teixeira, Jos\'e Miguel Urbano
https://arxiv.org/abs/2404.03060

Oscillatory free boundary problems in stochastic materials
We investigate a class of free boundary problems with oscillatory singularities within stochastic materials. Our main result yields sharp regularity estimates along the free boundary, provided the power of the singularity varies in a Dini-continuous fashion below a certain threshold. We also reveal an interesting repelling estimate preventing the free boundary from touching the region where the singularity power oscillates above the threshold.

This https://arxiv.org/abs/2402.06017 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Deformations of Zappatic stable surfaces and their Galois covers
This paper has an appendix, written by considers some algebraic surfaces that can deform to planar Zappatic stable surfaces with a unique singularity of type En. We prove that the Galois covers of these surfaces are all simply connected of general type, for n>=4, and we give a formula for Chern numbers of such Galois covers. As an application, we prove that such surfaces do not exist for n>30. Furthermore, Kollar improves the result to n>9 in Appendix 5.

2021 retro-link! https://bigthink.com/starts-with-a-bang/big-bang-beginning-universe/ - Did the Big Bang begin from a singularity? Not anymore.

The Nucleus of a Compact Lie Group, and Support of Singularity Categories
Thomas Peirce
https://arxiv.org/abs/2405.00457 https://arxi…

The Nucleus of a Compact Lie Group, and Support of Singularity Categories
In this paper we adapt the notion of the nucleus defined by Benson, Carlson, and Robinson to compact Lie groups in non-modular characteristic. We show that it describes the singularities of the projective scheme of the cohomology of its classifying space. A notion of support for singularity categories of ring spectra (in the sense of Greenlees and Stevenson) is established, and is shown to be precisely the nucleus in this case, consistent with a conjecture of Benson and Greenlees for finite gro…

This https://arxiv.org/abs/2403.18265 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

A Deep Learning Framework for Disentangling Triangle Singularity and Pole-Based Enhancements
Enhancements in the invariant mass distribution or scattering cross-section are usually associated with resonances. However, the nature of exotic signals found near hadron-hadron thresholds remain a puzzle today. In fact, a purely kinematic triangle mechanism is also capable of producing similar structures, but do not correspond to any unstable quantum state. In this paper, we report for the first time, that a deep neural network can be trained to distinguish triangle singularity from pole-base…

HPX with Spack and Singularity Containers: Evaluating Overheads for HPX/Kokkos using an astrophysics application
Patrick Diehl, Steven R. Brandt, Gregor Dai{\ss}, Hartmut Kaiser
https://arxiv.org/abs/2405.00016

HPX with Spack and Singularity Containers: Evaluating Overheads for HPX/Kokkos using an astrophysics application
Cloud computing for high performance computing resources is an emerging topic. This service is of interest to researchers who care about reproducible computing, for software packages with complex installations, and for companies or researchers who need the compute resources only occasionally or do not want to run and maintain a supercomputer on their own. The connection between HPC and containers is exemplified by the fact that Microsoft Azure's Eagle cloud service machine is number three on th…

Sad week ->
Vernor Vinge, father of the tech singularity, has died at age 79 | Ars Technica
https://arstechnica.com/information-technology/2024/03/vernor-vinge-father-of-the-tech-singularity-has-died-a…

Vernor Vinge, father of the tech singularity, has died at age 79
Vinge won multiple Hugo awards and created a sci-fi concept that drives AI researchers.

One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results
Oleksandr Gamayun, Oleg Lychkovskiy
https://arxiv.org/abs/2404.02099

One-dimensional Fermi polaron after a kick: two-sided singularity of the momentum distribution, Bragg reflection and other exact results
A mobile impurity particle immersed in a quantum fluid forms a polaron - a quasiparticle consisting of the impurity and a local disturbance of the fluid around it. We ask what happens to a one-dimensional polaron after a kick, i.e. an abrupt application of a force that instantly delivers a finite impulse to the impurity. In the framework of an integrable model describing an impurity in a one-dimensional gas of fermions or hard-core bosons, we calculate the distribution of the polaron momentum e…

RIP Vernor Vinge.
The Zones of Thought novels are some of my favorite space operas, with ideas as challenging and characters as memorable as any science fiction I've read.
https://transfer-orbit.ghost.io/vernor-vinge-singularity-scie…

2021 retro-link! https://bigthink.com/starts-with-a-bang/big-bang-beginning-universe/ - Did the Big Bang begin from a singularity? Not anymore.

The Nucleus of a Compact Lie Group, and Support of Singularity Categories
Thomas Peirce
https://arxiv.org/abs/2405.00457 https://arxi…

The Nucleus of a Compact Lie Group, and Support of Singularity Categories
In this paper we adapt the notion of the nucleus defined by Benson, Carlson, and Robinson to compact Lie groups in non-modular characteristic. We show that it describes the singularities of the projective scheme of the cohomology of its classifying space. A notion of support for singularity categories of ring spectra (in the sense of Greenlees and Stevenson) is established, and is shown to be precisely the nucleus in this case, consistent with a conjecture of Benson and Greenlees for finite gro…

This https://arxiv.org/abs/2309.01817 has been replaced.
link: https://scholar.google.com/scholar?q=a

Invariants and reversibility in polynomial systems of ODEs
This paper explores a relationship between invariants of certain group actions and the time-reversibility of two-dimensional polynomial differential systems exhibiting a $1:-1$ resonant singularity at the origin. We focus on the connection of time-reversibility with the Sibirsky subvariety of the center (integrability) variety, which encompasses systems possessing a local analytic first integral near the origin. An algorithm for generating the Sibirsky ideal for these systems is proposed and th…

Classification of simple 0-dimensional isolated complete intersection singularities
Thuy Huong Pham, Gerhard Pfister, Gert-Martin Greuel
https://arxiv.org/abs/2404.19728

Classification of simple 0-dimensional isolated complete intersection singularities
The aim of this article is the classification of simple 0-dimensional isolated complete intersection singularities in positive characteristic. As usual, a singularity is called simple or 0-modal if there are only finitely many isomorphism classes of singularities into which the given singularity can deform. The notion of simpleness was introduced by V. I. Arnold and the classification of low modality singularities has become a fundamental task in singularity theory. Simple complex analytic isol…

Logarithmic singularity in the density four-point function of two-dimensional critical percolation in the bulk
Federico Camia, Yu Feng
https://arxiv.org/abs/2403.18576

Logarithmic singularity in the density four-point function of two-dimensional critical percolation in the bulk
We provide definitive proof of the logarithmic nature of the percolation conformal field theory in the bulk by showing that the four-point function of the density operator has a logarithmic divergence as two points collide and that the same divergence appears in the operator product expansion (OPE) of two density operators. The right hand side of the OPE contains two operators with the same scaling dimension, one of them multiplied by a term with a logarithmic singularity. Our method involves a…

Singularity: a Seventh Memo?
Matteo Gallone, Sandra Lucente
https://arxiv.org/abs/2403.18487 https://arxiv.org/pdf/2403.18487<…

Singularity: a Seventh Memo?
In this paper we explore the relationships between Calvino's memos and Mathematics. In the first part, we discuss how Lightness, Quickness, Exactitude, Visibility, Multiplicity are present in the mathematical language, reasoning and in the work of the mathematician. In addiction, we follow a similar path for the topics of Calvino's lecture of which we only know the title or some notes. In the final part, we explain why `Singularity' could be chosen as topic for Calvino's seventh lecture.

This https://arxiv.org/abs/2302.05273 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On codimension one stability of the soliton for the 1D focusing cubic Klein-Gordon equation
We consider the codimension one asymptotic stability problem for the soliton of the focusing cubic Klein-Gordon equation on the line under even perturbations. The main obstruction to full asymptotic stability on the center-stable manifold is a small divisor in a quadratic source term of the perturbation equation. This singularity is due to the threshold resonance of the linearized operator and the absence of null structure in the nonlinearity. The threshold resonance of the linearized operator …

This https://arxiv.org/abs/2401.02228 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Infinite-Time Singularities of the Lagrangian Mean Curvature Flow
In this paper, we construct solutions of Lagrangian mean curvature flow which exist and are embedded for all time, but form an infinite-time singularity and converge to an immersed special Lagrangian as $t\to\infty$. In particular, the flow decomposes the initial data into a union of special Lagrangians intersecting at one point. This result shows that infinite-time singularities can form in the Thomas--Yau `semi-stable' situation. A precise polynomial blow-up rate of the second fundamental for…

This https://arxiv.org/abs/2304.01847 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Isolated hypersurface singularities, spectral invariants, and quantum cohomology
We study the relation between isolated hypersurface singularities (e.g. ADE) and the quantum cohomology ring by using spectral invariants, which are symplectic invariants coming from Floer theory. We prove, under the assumption that the quantum cohomology ring is semi-simple, that (1) if the smooth Fano variety (or the symplectic manifold) degenerates to a Fano variety with an isolated hypersurface singularity, then the singularity has to be an $A_m$-singularity, (2) if the symplectic manifold …

A Revisit to Classical and Quantum aspects of Raychaudhuri equation and possible resolution of Singularity
Subenoy Chakraborty, Madhukrishna Chakraborty
https://arxiv.org/abs/2402.17799

A Revisit to Classical and Quantum aspects of Raychaudhuri equation and possible resolution of Singularity
In this review, we provide a concrete overview of the Raychaudhuri equation, Focusing theorem and Convergence conditions in a plethora of backgrounds and discuss the consequences. We also present various classical and quantum approaches suggested in the literature that could potentially mitigate the initial big-bang singularity and the black-hole singularity.

Here is a sneak preview of my latest—on "California Forever" (the Solano County tech city), AI images, Thomas Kinkade, Christian Eschatology, the Singularity, and more—written only for you and me, not for some scurrilous, paywalled academic publication.
https://varnelis.net/cal…

California Forever or, the Aesthetics of AI images
This past August (2023), a new urban project called “California Forever” was announced, promising a walkable city for 400,000 in Solano County, not far from the Bay area. Critics soon pointed out several flaws in the renderings the company distributed. First, even though the venture was backed by billionaire Silicon Valley investors such as Laurene ... Read more

Triangle singularity in the $J/\psi \to \phi \pi^ a_0^-(\pi^- \eta),\; \phi \pi^- a_0^ (\pi^ \eta)$ decays
C. W. Xiao, J. M. Dias, L. R. Dai, W. H. Liang, E. Oset
https://arxiv.org/abs/2402.17584

Triangle singularity in the $J/ψ\to ϕπ^+ a_0^-(π^- η),\; ϕπ^- a_0^+(π^+ η)$ decays
We study the $J/ψ\to ϕπ^+ a_0(980)^- (a_0^- \to π^- η)$ decay, evaluating the double mass distribution in terms of the $π^- η$ and $π^+ a_0$ invariant masses. We show that the $π^- η$ mass distribution exhibits the typical cusp structure of the $a_0(980)$ seen in recent high statistics experiments, and the $π^+ a_0$ spectrum shows clearly a peak around $M_{\rm inv}(π^+ a_0)=1420 \,{\rm MeV}$, corresponding to a triangle singularity. When integrating over the two invariant masses we …

Domar aggregation under nonneutral elasticity of substitution
Satoshi Nakano, Kazuhiko Nishimura
https://arxiv.org/abs/2404.18137 https://

Domar aggregation under nonneutral elasticity of substitution
The characteristics inherent in a Domar aggregation, when all sectoral productions embody a common nonneutral elasticity of substitution, is examined. There, the general equilibrium propagation of productivity changes entails structural transformation that brings nonlinearities in their aggregation into price indices. We show that negative singularity, such that a finite productivity decrease induces an infinitely large price, is possible in an inelastic economy, while positive singularity, suc…

The singularity is closer than you think.

The Classical Point Particle Singularity: An Illusion in GR and Elsewhere!
Yousef Sobouti, Haidar Sheikhahmadi
https://arxiv.org/abs/2404.18954 https://

The Classical Point Particle Singularity: An Illusion in GR and Elsewhere!
Singularities in Newton's gravity, in general relativity, GR, in Coulomb's law, and elsewhere in classical physics, stem from two ill conceived assumptions that, a) there are point-like entities with finite masses, charges, etc., packed in zero volumes, and b) the non-quantum assumption that these point-like entities can be assigned precise coordinates and momenta. In the case of GR, we argue that the classical energy-momentum tensor in Einstein's field equation is that of a collection of point…

This https://arxiv.org/abs/2309.05402 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The class group of a minimal model of a quotient singularity
Let $V$ be a finite-dimensional vector space over the complex numbers and let $G\leq \operatorname{SL}(V)$ be a finite group. We describe the class group of a minimal model (that is, $\mathbb Q$-factorial terminalization) of the linear quotient $V/G$. We prove that such a class group is completely controlled by the junior elements contained in $G$.

This https://arxiv.org/abs/2304.14056 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Lévy-type operators with low singularity kernels: regularity estimates and martingale problem
We consider the linear non-local operator $\mathcal{L}$ denoted by \[ \mathcal{L} u (x) = \int_{\mathbb{R}^d} \left(u(x+z)-u(x)\right) a(x,z)J(z)\,d z. \] Here $a(x,z)$ is bounded and $J(z)$ is the jumping kernel of a Lévy process, which only has a low-order singularity near the origin and does not allow for standard scaling. The aim of this work is twofold. Firstly, we introduce generalized Orlicz-Besov spaces tailored to accommodate the analysis of elliptic equations associated with $\mathca…

Giant Strain Response of Charge Modulation and Singularity in a Kagome Superconductor
Chun Lin, Armando Consiglio, Ola Kenji Forslund, Julia Kuspert, M. Michael Denner, Hechang Lei, Alex Louat, Matthew D. Watson, Timur K. Kim, Cephise Cacho, Dina Carbone, Mats Leandersson, Craig Polley, Thiagarajan Balasubramanian, Domenico Di Sante, Ronny Thomale, Zurab Guguchia, Giorgio Sangiovanni, Titus Neupert, Johan Chang

Giant Strain Response of Charge Modulation and Singularity in a Kagome Superconductor
Tunable quantum materials hold great potential for applications. Of special interest are materials in which small lattice strain induces giant electronic responses. The kagome compounds AV3Sb5 (A = K, Rb, Cs) provide a testbed for such singular electronic states. In this study, through angle-resolved photoemission spectroscopy, we provide comprehensive spectroscopic measurements of the giant responses induced by compressive and tensile strains on the charge-density-wave (CDW) order parameter an…

This https://arxiv.org/abs/2209.14090 has been replaced.
link: https://scholar.google.com/scholar?q=a

Enhanced Auslander-Reiten duality and Morita theorem for singularity categories
We establish a Morita theorem to construct triangle equivalences between the singularity categories of (commutative and non-commutative) Gorenstein rings and the cluster categories of finite dimensional algebras over fields, and more strongly, quasi-equivalences between their canonical dg enhancements. More precisely, we prove that such an equivalence exists as soon as we find a quasi-equivalence between the graded dg singularity category of a Gorenstein ring and the derived category of a finit…

A Revisit to Classical and Quantum aspects of Raychaudhuri equation and possible resolution of Singularity
Subenoy Chakraborty, Madhukrishna Chakraborty
https://arxiv.org/abs/2402.17799

A Revisit to Classical and Quantum aspects of Raychaudhuri equation and possible resolution of Singularity
In this review, we provide a concrete overview of the Raychaudhuri equation, Focusing theorem and Convergence conditions in a plethora of backgrounds and discuss the consequences. We also present various classical and quantum approaches suggested in the literature that could potentially mitigate the initial big-bang singularity and the black-hole singularity.

This https://arxiv.org/abs/2309.00607 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

The ALE Partition Functions of M-Strings
We compute the equivariant partition function of the six-dimensional M-string SCFTs on a background with the topology of a product of a two-dimensional torus and an ALE singularity. We determine the result by exploiting BPS strings probing the singularity, whose worldvolume theories we determine via a chain of string dualities. A distinguished feature we observe is that for this class of background the BPS strings' worldsheet theories become relative field theories that are sensitive to finer d…

Visualizing orbital angular momentum induced single wavefront dislocation in graphene
Yi-Wen Liu, Yu-Chen Zhuang, Ya-Ning Ren, Chao Yan, Xiao-Feng Zhou, Qian Yang, Qing-Feng Sun, Lin He
https://arxiv.org/abs/2403.19767

Visualizing orbital angular momentum induced single wavefront dislocation in graphene
Phase singularities are phase-indeterminate points where wave amplitudes are zero, which manifest as phase vertices or wavefront dislocations. In the realm of optical and electron beams, the phase singularity has been extensively explored, demonstrating a profound connection to orbital angular momentum. Direct local imaging of the impact of orbital angular momentum on phase singularities at the nanoscale, however, remains a challenge and has yet to be achieved. Here, we study the role of orbita…

Why is it so hard to understand that "ai will make 30% of workers redundant" is *in itself* a catastrophe for everybody else as well?
That is the singularity we're running into, not some bullshit AGI awakening, but I feel like nobody is even considering that.

This https://arxiv.org/abs/2402.11315 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Rigidity aspects of Penrose's singularity theorem
In this paper, we study rigidity aspects of Penrose's singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose's singularity theorem except with weakly trapped surfaces instead of trapped surfaces, then what can be said about the global spacetime structure if the spacetime is null geodesically complete? In this setting, we show that we obtain a foliation of MOTS which generate totally geodesic null hypersurfaces. Depending on…

Formal Poisson (co)homology of the Lefschetz singularity
Lauran Toussaint, Florian Zeiser
https://arxiv.org/abs/2403.16300 https://ar…

Formal Poisson (co)homology of the Lefschetz singularity
We compute the formal Poisson cohomology groups of a real Poisson structure $π$ on $\mathbb{C}^2$ associated to the Lefschetz singularity $(z_1, z_2)\mapsto z_1^2+z_2^2$. In particular we correct an erroneous computation in the literature. The definition of $π$ depends on a choice of volume form. Using the main result we formally classify all Poisson structure arising from different choices of volume forms.

Reading the log canonical threshold of a plane curve singularity from its Newton polyhedron
Erik Paemurru
https://arxiv.org/abs/2404.18238 https://<…

Reading the log canonical threshold of a plane curve singularity from its Newton polyhedron
There is a proposition due to Kollár 1997 on computing log canonical thresholds of certain hypersurface germs using weighted blowups, which we extend to weighted blowups with non-negative weights. Using this, we show that the log canonical threshold of a convergent complex power series is at most $1/c$, where $(c, \ldots, c)$ is a point on a facet of its Newton polyhedron. Moreover, in the case $n = 2$, if the power series is weakly normalised with respect to this facet or the point $(c, c)$ b…

I’ve been following the Social Media Sameness Singularity since 2016.
It’s sometimes also corporate espionage!
From: @…
https://mastodon.social/@arstechni…

Ars Technica (@arstechnica@mastodon.social)
Attached: 1 image Facebook secretly spied on Snapchat usage to confuse advertisers, court docs say Zuckerberg told execs to “figure out” how to spy on encrypted Snapchat traffic. https://arstechnica.com/tech-policy/2024/03/facebook-secretly-spied-on-snapchat-usage-to-confuse-advertisers-court-docs-say/?utm_brand=arstechnica&utm_social-type=owned&utm_source=mastodon&utm_medium=social

Exact calculation of degrees for lattice equations: a singularity approach
Takafumi Mase
https://arxiv.org/abs/2402.16206 https://arx…

Exact calculation of degrees for lattice equations: a singularity approach
The theory of degree growth and algebraic entropy plays a crucial role in the field of discrete integrable systems. However, a general method for calculating degree growth for lattice equations (partial difference equations) is not yet known. Here we propose a new method to rigorously compute the exact degree of each iterate for lattice equations. Our strategy is to extend Halburd's method, which is a novel approach to computing the exact degree of each iterate for mappings (ordinary difference…

A Deep Learning Framework for Disentangling Triangle Singularity and Pole-Based Enhancements
Darwin Alexander O. Co, Vince Angelo A. Chavez, Denny Lane B. Sombillo
https://arxiv.org/abs/2403.18265

A Deep Learning Framework for Disentangling Triangle Singularity and Pole-Based Enhancements
Enhancements in the invariant mass distribution or scattering cross-section are usually associated with resonances. However, the nature of exotic signals found near hadron-hadron thresholds remain a puzzle today. In fact, a purely kinematic triangle mechanism is also capable of producing similar structures, but do not correspond to any unstable quantum state. In this paper, we report for the first time, that a deep neural network can be trained to distinguish triangle singularity from pole-base…

Ok I was a skeptic but the video demo of this new ML paper has me convinced. The world as we know it is over, the singularity will be here by the end of Q2. Just look at this: https://youtu.be/sJNK4VKeoBM?si=X3XdDUOcx0ynvs1q

Singular equivalence and singular locus
Leilei Liu, Jieheng Zeng
https://arxiv.org/abs/2403.13637 https://arxiv.org/pdf/2403.13637

Singular equivalence and singular locus
For a commutative Gorenstein Noetherian ring $R$, we construct an affine scheme $X$ solely from singularity category $D_{sg}(R)$ of $R$ such that there is a finite surjective morphism $X \rightarrow \mathrm{Spec}(R /I)$, where $\mathrm{Spec}(R /I)$ is the singular locus in $\mathrm{Spec}(R)$. As an application, for two such rings with equivalent singularity categories, we prove that the singular loci in their affine schemes have the same dimension.

This https://arxiv.org/abs/2309.15271 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Kinematic Modularity of Elementary Dynamic Actions
In this paper, a kinematically modular approach to robot control is presented. The method involves structures called Elementary Dynamic Actions and a network model combining these elements. With this control framework, a rich repertoire of movements can be generated by combination of basic modules. The problems of solving inverse kinematics, managing kinematic singularity and kinematic redundancy are avoided. The modular approach is robust against contact and physical interaction, which makes i…

On regularity and rigidity of $2\times 2$ differential inclusions into non-elliptic curves
Xavier Lamy, Andrew Lorent, Guanying Peng
https://arxiv.org/abs/2404.02121

On regularity and rigidity of $2\times 2$ differential inclusions into non-elliptic curves
We study differential inclusions $Du\in Π$ in an open set $Ω\subset\mathbb R^2$, where $Π\subset \mathbb R^{2\times 2}$ is a compact connected $C^2$ curve without rank-one connections, but non-elliptic: tangent lines to $Π$ may have rank-one connections, so that classical regularity and rigidity results do not apply. For a wide class of such curves $Π$, we show that $Du$ is locally Lipschitz outside a discrete set, and is rigidly characterized around each singularity. Moreover, in the part…

Negatively enhanced thermopower near a Van Hove singularity in electron-doped Sr$_2$RuO$_4$
Rei Nishinakayama, Yoshiki J. Sato, Takayoshi Yamanaka, Yoshiteru Maeno, Hiroshi Yaguchi, Naoki Kikugawa, Ryuji Okazaki
https://arxiv.org/abs/2404.11300

Negatively enhanced thermopower near a Van Hove singularity in electron-doped Sr$_2$RuO$_4$
The layered perovskite Sr$_2$RuO$_4$ serves as a model material of the two-dimensional (2D) Fermi liquid but also exhibits various emergent phenomena including the non-Fermi-liquid (NFL) behavior under external perturbations such as uniaxial pressure and chemical substitutions. Here we present the thermoelectric transport of electron-doped system Sr$_{2-y}$La$_{y}$RuO$_4$, in which a filling-induced Lifshitz transition occurs at the Van Hove singularity (VHS) point of $y\approx 0.2$. We find th…

I’m gonna decline that trade…
The #TESCREAL billionaire fascination with virtual immortality is grounded in juvenile cowardice & narcissism. Humans die. All of us. Humans age. All of us. Our *minds* age, both because of our brains aging & because we have experiences which include other humans close to us dying. Nothing can be forever.
It's a pharaonic impulse to build a monu…

Emergent dynamics of the inertial Kuramoto model with frustration on a locally coupled graph
Tingting Zhu, Xiongtao Zhang
https://arxiv.org/abs/2404.18488 …

Emergent dynamics of the inertial Kuramoto model with frustration on a locally coupled graph
We study the synchronized behavior of the inertial Kuramoto oscillators with frustration effect under a symmetric and connected network. Due to the lack of second-order gradient flow structure and singularity of second-order derivative of diameter, we shift to construct convex combinations of oscillators and related new energy functions that can control the phase and frequency diameters. Under sufficient frameworks on initial data and system parameters, we derive first-order dissipative differe…

This https://arxiv.org/abs/2310.01734 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

New models of $4D$ and Extra dimensional black holes without inner horizon and with an integrable singularity
The inclusion of localized sources of matter (LSM) in the energy-momentum tensor has been widely utilised in constructing regular black holes (RBHs). In \cite{Casadio:2023iqt}, it is established that in $4D$, an energy density behaving as $r^{-2}$ near the origin leads to a black hole solution with a central integrable singularity and without an inner horizon. In this manuscript, we generalize this result, establishing the conditions that the energy density and the solution must satisfy both in…

This https://arxiv.org/abs/2204.07896 has been replaced.
link: https://scholar.google.com/scholar?q=a

Generic regularity of Level Set Flows with spherical singularity
The sphere is well-known as the only generic compact shrinker for mean curvature flow (MCF). In this paper, we characterize the generic dynamics of MCFs with a spherical singularity. In terms of the level set flow formulation of MCF, we establish that generically the arrival time function of level set flow with spherical singularity has at most $C^2$ regularity.

This https://arxiv.org/abs/2303.08802 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Review of the No-Boundary Wave Function
When the universe is treated as a quantum system, it is described by a wave function. This wave function is a function not only of the matter fields, but also of spacetime. The no-boundary proposal is the idea that the wave function should be calculated by summing over geometries that have no boundary to the past, and over regular matter configurations on these geometries. Accordingly, the universe is finite, self-contained and the big bang singularity is avoided. Moreover, given a dynamical th…

This https://arxiv.org/abs/2402.15156 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Spacetime singularities and caustic of outgoing null hypersurfaces
In this paper, we investigate the caustic point developed by outgoing null hypersurfaces and the behavior of null curves. We analyze three cases: Future, past, and zero caustic point terminology for outgoing null hypersurfaces in the marginally bound Lemaitre-Tolman-Bondi (LTB) metric for homogenous and inhomogeneous cases defined in the present work. We show the criteria to form local and globally visible singularity in terms of the tangent on the apparent horizon curve.

Disentangling mappings defined on ICIS
Alberto Fern\'andez-Hern\'andez
https://arxiv.org/abs/2403.19678 https://arxiv.org/pdf…

Disentangling mappings defined on ICIS
Let $(X,S)$ be an isolated complete intersection singularity of dimension $n$, and let $f:(X,S)\rightarrow (\mathbb{C}^{n+1},0)$ be a germ of $\mathscr{A}$-finite mapping. In this master's degree final project, our main contribution is that we show the case $n=2$ of the general Mond conjecture, which states that $μ_I(X,f)\geq \text{codim}_{\mathscr{A}_e}(X,f)$, with equality provided $(X,f)$ is weighted homogeneous. Before this project, the only known case for which the conjecture was known to…

This https://arxiv.org/abs/2404.07830 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetry
In this paper, we define the rarefaction and compression characters for the supersonic expanding wave of the compressible Euler equations with radial symmetry. Under this new definition, we show that solutions with rarefaction initial data will not form shock in finite time, i.e. exist global-in-time as classical solutions. On the other hand, singularity forms in finite time when the initial data include strong compression somewhere. Several useful invariant domains will be also given.

This https://arxiv.org/abs/2302.13249 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture
We show that the specialized quantum D-module of the equivariant quantum cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the D-module of graded traces on the minimal nilpotent orbit in the Lie algebra of the same type. This generalizes a recent result of Shlykov [Hikita conjecture for the minimal nilpotent orbit, to appear in Proc. AMS, https://doi.org/10.1090/proc/15281] and hence verifies in this case the quantum version of Hikita's conjecture, proposed by Kam…

Geometry on deformations of S1 singularities
Runa Shimada
https://arxiv.org/abs/2404.17172 https://arxiv.org/pdf/2404.17172
arXiv:2404.17172v1 Announce Type: new
Abstract: For a one parameter deformation of the $S_1$ singularity in the three space, we give a form using only isometric maps of the target. Using this form, we study differential geometric properties of $S_1$ singularities and the Whitney umbrellas appearing in the deformation.

Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes
Petr \v{C}oupek, Pavel K\v{r}\'i\v{z}, Bohdan Maslowski
https://arxiv.org/abs/2403.12610

Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes
In this paper, we study parameter identification for solutions to (possibly non-linear) SDEs driven by additive Rosenblatt process and singularity of the induced laws on the path space. We propose a joint estimator for the drift parameter, diffusion intensity, and Hurst index that can be computed from discrete-time observations with a bounded time horizon and we prove its strong consistency (as well as the speed of convergence) under in-fill asymptotics with a fixed time horizon. As a consequen…

This https://arxiv.org/abs/2002.08706 has been replaced.
link: https://scholar.google.com/scholar?q=a

Lojasiewicz exponent of a surface: an intrinsic view
In this paper we observe that the Łojasiewicz exponent $\mathcal{L}_0(X)$ of an ADE-type singularity $X$ can be computed by means of invariants of certain ideals in the local ring ${\mathcal O}_{X,0}$. After extending the notion of Łojasiewicz exponent to rational singularities of higher multiplicities we make a similar observation for RTP-type singularities.

On standing wave in perturbed anti-de Sitter spacetimes with a naked singularity
Kai Lin, Wei-Liang Qian
https://arxiv.org/abs/2404.16254 https://

On standing wave in perturbed anti-de Sitter spacetimes with a naked singularity
In the framework of black hole perturbation theory, this work investigates the standing wave solutions in Reissner-Nordtsröm (RN) anti-de Sitter (AdS) spacetimes with a naked singularity. These solutions can be viewed as a specific class of quasinormal modes exhibiting distinct characteristics. The imaginary parts of their frequencies are numerically vanishing, allowing them to persist over an extended period. Besides, these modes are predominantly stationary in terms of the evolution of space…

This https://arxiv.org/abs/2404.14816 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Regular black holes as an alternative to black bounce
The so-called black bounce mechanism of singularity suppression, proposed by Simpson and Visser, consists in replacing the spherical radius $r$ in the metric tensor with $\sqrt{r^2 + a^2}$, $a = \rm const >0$. This removes a singularity at $r=0$ and its neighborhood from space-time, and there emerges a regular minimum of the spherical radius that can be a wormhole throat or a regular bounce (if located inside a black hole). Instead, it is proposed here to make $r=0$ a regular center by proper (…

Singular equivalences induced by ring extensions
Yongyun Qin
https://arxiv.org/abs/2403.12412 https://arxiv.org/pdf/2403.12412…

Singular equivalences induced by ring extensions
Let $B \subseteq A$ be an extension of finite dimensional algebras. We provide a sufficient condition for the existence of triangle equivalences of singularity categories (resp. Gorenstein defect categories) between $A$ and $B$. This result is applied to trivial extensions, Morita rings and triangular matrix algebras to give several reduction methods on singularity categories and Gorenstein defect categories of algebras.

Twisted Koszul algebras of nonisolated hypersurface singularities
Sangwook Lee
https://arxiv.org/abs/2402.17965 https://arxiv.org/pdf…

Twisted Koszul algebras of nonisolated hypersurface singularities
Given a hypersurface singularity (not necessarily isolated) with a finite abelian group action, we develop a method to define an explicit product structure on the twisted Koszul algebra (whose invariant subalgebra is the orbifold Koszul algebra).

This https://arxiv.org/abs/2308.05240 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Local solvability and dilation-critical singularities of supercritical fractional heat equations
We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for local-in-time solvability. We introduce the notion of a dilation-critical singularity (DCS) of the initial data and show that such singularities always exist for a large class of supercritical nonlinearities. Moreover, we provide exact formulae for such singularities.

Non-perturbative quantum gravity denounces singular Black Holes
Alexey Koshelev, Anna Tokareva
https://arxiv.org/abs/2404.07925 https://

Non-perturbative quantum gravity denounces singular Black Holes
Although General Relativity predicts the presence of a singularity inside of a Black Hole, it is not a complete theory of gravity. A real structure of a Black Hole interior near an expected singularity depends on the UV completion of gravity. In this paper, we establish that the question whether singular spherically symmetric solutions are absent is governed by the functional form of a non-perturbative graviton propagator. We explicitly show in a framework of a ghost-free infinite derivative gr…

A tree formula for the ellipsoidal superpotential of the complex projective plane
Kyler Siegel
https://arxiv.org/abs/2404.14707 https://arxiv.org/pdf/2404.14707
arXiv:2404.14707v1 Announce Type: new
Abstract: The ellipsoidal superpotential of the complex projective plane can be interpreted as a count of rigid rational plane curves of a given degree with one prescribed cusp singularity. In this note we present a closed formula for these counts as a sum over trees with certain explicit weights. This is a step towards understanding the combinatorial underpinnings of the ellipsoidal superpotential and its mysterious nonvanishing and nondecreasing properties.

Research on high-frequency quasi-periodic oscillations in generalized black-bounce spacetime
Jianbo Lu, Shining Yang, Yuying Zhang, Liu Yang, Mou Xu
https://arxiv.org/abs/2403.19942

Research on high-frequency quasi-periodic oscillations in generalized black-bounce spacetime
In order to solve problem of spacetime singularity in theoretical physics, researchers proposed the regular black holes (BH). The generalized black-bounce (GBB) spacetime, as a unified treatment of distinct kinds of geometries in the framework of general relativity (e.g. regular BH and wormholes), has been extensively studied. Firstly, we derive to give the explicit forms of Lagrangian for a nonlinear electromagnetic field and potential for a non-canonical phantom field in the action of gravita…

This https://arxiv.org/abs/2402.15660 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Toric resolutions of strongly mixed weighted homogeneous polynomial germs of type $J_{10}^-$
We consider toric resolutions of some strongly mixed weighted homogeneous polynomials of type $J_{10}^-$. We show that the strongly mixed weighted homogeneous polynomial $f := f_{2,2,1,2,1,4}\ (k=3)$ (see §3) has no mixed critical points on ${\mathbb{C}^*}^2$ (Lemma 14), and moreover, show that the strict transform $\tilde V$ of the mixed hypersurface singularity $V := f^{-1}(0)$ via the toric modification $\hatπ : X \to \mathbb{C}^2$, where we set $f := f_{2,2,1,2,1,4}\ (k=3)$, is not only a…

This https://arxiv.org/abs/2304.03444 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A conformal heat flow for harmonic maps does not develop finite time bubbling
A conformal heat flow for harmonic maps is a system of evolution equations combined with harmonic map flow with metric evolution in conformal direction. It is known that global weak solution of the flow exists and smooth except at mostly finitely many singular points. In this paper, we show that finite time singularity does not occur, unlike usual harmonic map flow.

Non-perturbative quantum gravity denounces singular Black Holes
Alexey Koshelev, Anna Tokareva
https://arxiv.org/abs/2404.07925 https://

Non-perturbative quantum gravity denounces singular Black Holes
Although General Relativity predicts the presence of a singularity inside of a Black Hole, it is not a complete theory of gravity. A real structure of a Black Hole interior near an expected singularity depends on the UV completion of gravity. In this paper, we establish that the question whether singular spherically symmetric solutions are absent is governed by the functional form of a non-perturbative graviton propagator. We explicitly show in a framework of a ghost-free infinite derivative gr…

The multiplicity of cyclic coverings of a singularity of an algebraic variety
Toya Kumagai, Tomohiro Okuma
https://arxiv.org/abs/2403.14355 https://…

The multiplicity of cyclic coverings of a singularity of an algebraic variety
Let $V$ be an affine algebraic variety, and let $p\in V$ be a singular point. For a regular function $g$ on $V$ such that $g(p)=0$ and for a positive integer $n$, we consider the cyclic covering $ϕ_n\: V_n \to V$ of degree $n$ branched along the hypersurface defined by $g$. We will prove that for sufficiently large $n$, the tangent cone of $V_n$ at $ϕ_n^{-1}(p)$ is, as an affine variety, the product of the tangent cone of the branch locus and the affine line. In particular, the multiplicity o…

Which shapes can appear in a Curve Shortening Flow Singularity?
Sigurd Angenent, Evan Patrick Davis, Ellie DeCleene, Paige Ellingson, Ziheng Feng, Edgar Gevorgyan, Aris Lemmenes, Alex Moon, Tyler Joseph Tommasi, Yamin Zhou
https://arxiv.org/abs/2403.09876

Which shapes can appear in a Curve Shortening Flow Singularity?
We study possible tangles that can occur in singularities of solutions to plane Curve Shortening Flow. We exhibit solutions in which more complicated tangles with more than one self-intersection disappear into a singular point. It seems that there are many examples of this kind and that a complete classification presents a problem similar to the problem of classifying all knots in $\mathbb R^3$. As a particular example, we introduce the so-called $n$-loop curves, which generalize Matt Grayson's…

This https://arxiv.org/abs/2404.10941 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Viscous shock waves of Burgers equation with fast diffusion and singularity
In this paper, we study the asymptotic stability of viscous shock waves for Burgers' equation with fast diffusion $u_t+f(u)_x=μ(u^m)_{xx}$ on $\mathbb{R} \times (0, +\infty)$ when $0u_+=0$, the equation with fast diffusion $(u^m)_{xx}=m\left(\frac{u_x}{u^{1-m}}\right)_x$ processes a strong singularity at $u_+=0$, which causes the stability study to be challenging. We observe that, there exist two different types of viscous shocks, one is the non-deg…

This https://arxiv.org/abs/2404.02940 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Tipler Naked Singularities in $N$ Dimensions
A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes in the approach of the singularity. It is called naked if it is the past endpoint of causal curves in spacetime. Here, we study the formation of strong curvature naked singularities arising from spherically symmetric gravitational collapse of general type-I ma…

This https://arxiv.org/abs/2307.01295 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hodge diamonds of the Landau--Ginzburg orbifolds
Consider the pairs $(f,G)$ with $f = f(x_1,\dots,x_N)$ being a polynomial defining a quasihomogeneous singularity and $G$ being a subgroup of $\mathrm{SL}(N,\mathbb{C})$, preserving $f$. In particular, $G$ is not necessarily abelian. Assume further that $G$ contains the grading operator $j_f$ and $f$ satisfies the Calabi-Yau condition. We prove that the nonvanishing bi-graded pieces of the B--model state space of $(f,G)$ form a diamond. We identify its top-most, bottom-most, left-most and right…

This https://arxiv.org/abs/2402.18785 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

On the semiclassical bounce with strong minimal assumptions
We explore the possibility of avoiding cosmological singularity with a bounce solution in the early Universe. The main finding is that simple and well-known semiclassical correction, which describes the mixing of radiation and gravity in the effective action, may provide an analytic solution with a bounce. The solution requires a positive beta function for the total radiation term and the contraction of the Universe at the initial instant. The numerical estimate shows that the bounce may occur …

This https://arxiv.org/abs/2310.03064 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Machine learning Sasakian and $G_2$ topology on contact Calabi-Yau $7$-manifolds
We propose a machine learning approach to study topological quantities related to the Sasakian and $G_2$-geometries of contact Calabi-Yau $7$-manifolds. Specifically, we compute datasets for certain Sasakian Hodge numbers and for the Crowley-Nördstrom invariant of the natural $G_2$-structure of the $7$-dimensional link of a weighted projective Calabi-Yau $3$-fold hypersurface singularity, for 7549 of the 7555 possible $\mathbb{P}^4(\textbf{w})$ projective spaces. These topological quantities a…

Closedness of the singular locus and generation for derived categories
Souvik Dey, Pat Lank
https://arxiv.org/abs/2403.19564 https://…

Closedness of the singular locus and generation for derived categories
This work is concerned with a relationship regarding the closedness of the singular locus of a Noetherian scheme and existence of classical generators in its category of coherent sheaves, associated bounded derived category, and singularity category. Particularly, we extend an observation initially made by Iyengar and Takahashi in the affine context to the global setting. Furthermore, we furnish an example a Noetherian scheme whose bounded derived category admits a classical generator, yet not …

Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetry
Geng Chen, Faris A. El-Katri, Yanbo Hu, Yannan Shen
https://arxiv.org/abs/2404.07830

Global solution and singularity formation for the supersonic expanding wave of compressible Euler equations with radial symmetry
In this paper, we define the rarefaction and compression characters for the supersonic expanding wave of the compressible Euler equations with radial symmetry. Under this new definition, we show that solutions with rarefaction initial data will not form shock in finite time, i.e. exist global-in-time as classical solutions. On the other hand, singularity forms in finite time when the initial data include strong compression somewhere. Several useful invariant domains will be also given.

This https://arxiv.org/abs/2404.02940 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Tipler Naked Singularities in $N$ Dimensions
A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes in the approach of the singularity. It is called naked if it is the past endpoint of causal curves in spacetime. Here, we study the formation of strong curvature naked singularities arising from spherically symmetric gravitational collapse of general type-I ma…

Toric resolutions of strongly mixed weighted homogeneous polynomial germs of type $J_{10}^-$
Sachiko Saito
https://arxiv.org/abs/2402.15660 https://…

Toric resolutions of strongly mixed weighted homogeneous polynomial germs of type $J_{10}^-$
We consider toric resolutions of some strongly mixed weighted homogeneous polynomials of type $J_{10}^-$. We show that the strongly mixed weighted homogeneous polynomial $f := f_{2,2,1,2,1,4}\ (k=3)$ (see §3) has no mixed critical points on ${\mathbb{C}^*}^2$ (Lemma 14), and moreover, show that the strict transform $\tilde V$ of the mixed hypersurface singularity $V := f^{-1}(0)$ via the toric modification $\hatπ : X \to \mathbb{C}^2$, where we set $f := f_{2,2,1,2,1,4}\ (k=3)$, is not only a…

This https://arxiv.org/abs/2401.11975 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Crossing the singularity of a gravitational wave collision
A reformulation of general relativity inspired by the Belinski-Khalatnikov-Lifshitz conjecture had been introduced by Ashtekar, Henderson and Sloan which is based on variables closely related to the basic variables of loop quantum gravity, thereby providing a way of classically analyzing singularities that may be carried over to the quantum theory. It is reasonable to expect that these variables are regular at generic spacelike singularities. This has been shown on various examples -- particula…

Asymptotic expansions for conformal scalar curvature equations near isolated singularities
Xusheng Du, Hui Yang
https://arxiv.org/abs/2402.16597 https://…

Asymptotic expansions for conformal scalar curvature equations near isolated singularities
In this paper, we study asymptotic expansions of positive solutions of the conformal scalar curvature equation $$ - Δu = K(x) u^\frac{n + 2}{n - 2} ~~~~~~ \textmd{in} ~ B_1 \setminus \{ 0 \} $$ with an isolated singularity at the origin. Under certain flatness conditions on $K$, we establish a higher-order expansion of solutions near the origin. In particular, we give the refined second-order asymptotic expansion of solutions when $n \geq 6$. Moreover, we also obtain an arbitrary-order expansi…

This https://arxiv.org/abs/2403.16741 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Spherically symmetric configurations in the quadratic $f(R)$ gravity
We study spherically symmetric configurations of the quadratic $f(R)$ gravity in the Einstein frame. In case of a purely gravitational system, we have determined the global qualitative behavior of the metric and the scalaron field for all static solutions satisfying the conditions of asymptotic flatness. These solutions are proved to be regular everywhere except for a naked singularity at the center; they are uniquely determined by the total mass $\mathfrak{M}$ and the "scalar charge" $Q$ chara…

This https://arxiv.org/abs/1310.2781 has been replaced.
link: https://scholar.google.com/scholar?q=a<…

The Euler number of the Jacobi factor of a plane curve singularity whose semigroup is $\langle4,6,13\rangle$
Piontkowski calculated the Euler number of Jacobi factors of plane curve singularities with semigroups $< p, q>$, $< 4, 2q, s>$, $< 6,8,s>$ and $< 6,10, s>$. %His analysis was done by decomposing the Jacobi factors into affine cells. In this paper, we show that a Jacobi factor for any curve singularity admits a cell decomposition by virtue of Pfister and Steenbrink's theory for punctual Hilbert schemes. We also introduce a computational method to determine the number of affine cells in the deco…

This https://arxiv.org/abs/2310.04157 has been replaced.
link: https://scholar.google.com/scholar?q=a

Particle motion in a rotating dust spacetime: the Bonnor solution
We investigate the geometrical properties, spectral classification, geodesics, and causal structure of the Bonnor's spacetime [Journal of Physics A Math. Gen., \textbf{10}, 1673 (1977)], i.e., a stationary axisymmetric solution with a rotating dust as a source. This spacetime has a directional singularity at the origin of the coordinates (related to the diverging vorticity field of the fluid there), which is surrounded by a toroidal region where closed timelike curves (CTCs) are allowed, leadin…

Motivic Hilbert zeta functions for curve singularities and related invariants
Masahiro Watari
https://arxiv.org/abs/2403.12545 https://

Motivic Hilbert zeta functions for curve singularities and related invariants
In the present paper, we show that the motivic Hilbert zeta function for a curve singularity yields the generating functions for Euler numbers of punctual Hilbert schemes when any punctual Hilbert scheme admits an affine cell decomposition. This fact allows us to derive the relations among the motivic Hilbert zeta function and other invariants such as the generating function for semi-modules of the semi-group of the singularity, the HOMFLY polynomial and the degrees of Severi strata of the mini…

This https://arxiv.org/abs/2311.15671 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

The generalized Vaidya spacetime with polytropic equation of state
The process of the gravitational collapse might lead not only to a black hole but also to naked singularity formation. In this paper, we consider the generalized Vaidya spacetime with polytropic and generalized polytropic equations of state. We solve the Einstein and Einstein-Maxwell equations to obtain the explicit form of a mass function. We consider the limiting cases of solutions and find out, that generalized Vaidya spacetime might behave like Vaidya-de Sitter and Bonnor-Vaidya-de sitter s…

Tian's stabilization problem for toric Fanos
Chenzi Jin, Yanir A. Rubinstein
https://arxiv.org/abs/2403.17262 https://arxiv.org/p…

Tian's stabilization problem for toric Fanos
In 1988, Tian posed the stabilization problem for equivariant global log canonical thresholds. We solve it in the case of toric Fano manifolds. This is the first general result on Tian's problem. A key new estimate involves expressing complex singularity exponents associated to orbits of a group action in terms of support and gauge functions from convex geometry. These techniques also yield a resolution of another conjecture of Tian from 2012 on more general thresholds associated to Grassmannia…

Tian's stabilization problem for toric Fanos
Chenzi Jin, Yanir A. Rubinstein
https://arxiv.org/abs/2403.17262 https://arxiv.org/p…

Tian's stabilization problem for toric Fanos
In 1988, Tian posed the stabilization problem for equivariant global log canonical thresholds. We solve it in the case of toric Fano manifolds. This is the first general result on Tian's problem. A key new estimate involves expressing complex singularity exponents associated to orbits of a group action in terms of support and gauge functions from convex geometry. These techniques also yield a resolution of another conjecture of Tian from 2012 on more general thresholds associated to Grassmannia…

This https://arxiv.org/abs/2312.11131 has been replaced.
link: https://scholar.google.com/scholar?q=a

Towards classifying the interior dynamics of charged black holes with scalar hair
The study of the interior of hairy black holes has received significant attention recently. This paper builds upon our recent analytical approach to investigate the internal dynamics of charged black holes with scalar hair in general spacetime dimensions. The geometries of these hairy balck holes end at a spacelike singularity. We investigate the alternation of Kasner epoch at later interior times and obtain the analytic expression for two kinds of transformation, namely Kasner inversion and Ka…

Kasner Eons
Pablo Bueno, Pablo A. Cano, Robie A. Hennigar
https://arxiv.org/abs/2402.14912 https://arxiv.org/pdf/2402.14912

Kasner Eons
As shown in the classic work of Belinski, Khalatnikov and Lifshitz, the approach to a generic space-like singularity in general relativity consists of a sequence of eras and epochs in which the metric is locally Kasner, connected by brief transitions. When quantum gravity effects are included, we argue that a new type of transition arises, giving rise to Kasner eons: periods which are dominated by emergent physics at each energy scale. We comment on the different ways in which the Einsteinian e…

This https://arxiv.org/abs/2307.01295 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hodge diamonds of the Landau--Ginzburg orbifolds
Consider the pairs $(f,G)$ with $f = f(x_1,\dots,x_N)$ being a polynomial defining a quasihomogeneous singularity and $G$ being a subgroup of ${\rm SL}(N,\mathbb{C})$, preserving $f$. In particular, $G$ is not necessary abelian. Assume further that $G$ contains the grading operator $j_f$ and $f$ satisfies the Calabi-Yau condition. We prove that the nonvanishing bigraded pieces of the B-model state space of $(f,G)$ form a diamond. We identify its topmost, bottommost, leftmost and rightmost entri…

This https://arxiv.org/abs/2404.02940 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Tipler Naked Singularities in $N$ Dimensions
A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes in the approach of the singularity. It is called naked if it is the past endpoint of causal curves in spacetime. Here, we study the formation of strong curvature naked singularities arising from spherically symmetric gravitational collapse of general type-I ma…

This https://arxiv.org/abs/2404.02940 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Tipler Naked Singularities in $N$ Dimensions
A spacetime singularity, identified by the existence of incomplete causal geodesics in the spacetime, is called a (Tipler) strong curvature singularity if the volume form acting on independent Jacobi fields along causal geodesics vanishes in the approach of the singularity. It is called naked if it is the past endpoint of causal curves in spacetime. Here, we study the formation of strong curvature naked singularities arising from spherically symmetric gravitational collapse of general type-I ma…

This https://arxiv.org/abs/2312.05960 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Moduli spaces of framed sheaves on compactified Kleinian singularities
Consider a Kleinian singularity $ \mathbb{C}^2/Γ$, where $ Γ$ is a finite subgroup of $ SL_2(\mathbb{C}) $. In this paper, we construct moduli spaces of framed sheaves on a projective Deligne-Mumford stack compactifying the singularity, and we show that these moduli spaces are quasiprojective schemes.

Spacetime singularities and caustic of outgoing null hypersurfaces
Ashok B. Joshi
https://arxiv.org/abs/2402.15156 https://arxiv.org/…

Spacetime singularities and caustic of outgoing null hypersurfaces
In this paper, we investigate the caustic point developed by outgoing null hypersurfaces and the behavior of null curves. We analyze three cases: Future, past, and zero caustic point terminology for outgoing null hypersurfaces in the marginally bound Lemaitre-Tolman-Bondi (LTB) metric for homogenous and inhomogeneous cases defined in the present work. We show the criteria to form local and globally visible singularity in terms of the tangent on the apparent horizon curve.

The symplectic form associated to a singular Poisson algebra
Hans-Christian Herbig, William Osnayder Clavijo Esquivel
https://arxiv.org/abs/2403.14921 http…

The symplectic form associated to a singular Poisson algebra
Given an affine Poisson algebra, that is singular one may ask whether there is an associated symplectic form. In the smooth case the answer is obvious: for the symplectic form to exist the Poisson tensor has to be invertible. In the singular case, however, derivations do not form a projective module and it is less clear what non-degenerate means. For a symplectic singularity one may naively ask if there is indeed an analogue of a symplectic form. We examine an example of a symplectic singularit…

This https://arxiv.org/abs/2307.12096 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

The Interiors of Singularity-Free Rotating Black Holes
General Relativity provides us with some solutions for rotating black holes. However, there are some problems associated with them: the appearance of singularities, the possibility of violations of the cosmic censorship conjecture, the existence of regions where the mass acts repulsively and the violation of causality. Many authors consider that these problems reveal the existence of certain limits in the applicability of General Relativity. For instance, it is believed that the same existence …