arxiv_id stringlengths 9 16 | title stringlengths 0 284 | authors listlengths 1 1.74k | submission_date stringlengths 10 116 | comments stringlengths 0 611 | primary_subject stringclasses 148
values | subjects stringlengths 13 354 | doi stringlengths 26 62 | abstract stringlengths 22 3.93k | file_path stringlengths 23 46 |
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1412.6978 | Orbit parametrizations of theta characteristics on hypersurfaces over arbitrary fields | [
"Yasuhiro Ishitsuka"
] | 22 Dec 2014 (<a href="https://arxiv.org/abs/1412.6978v1">v1</a>), last revised 21 Jan 2015 (this version, v3) | 35 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1412.6978 | It is well-known that theta characteristics on smooth plane curves over a field of characteristic different from two are in bijection with certain smooth complete intersections of three quadrics. We generalize this bijection to possibly singular hypersurfaces of any dimension over arbitrary fields including those of ch... | math-31-part-2.zip/1412.6978.pdf |
1105.4108 | Abelian varieties and theta functions associated to compact Riemannian manifolds; constructions inspired by superstring theory | [
"Stefan Müller-Stach",
"Chris Peters",
"Vasudevan Srinivas"
] | 20 May 2011 (<a href="https://arxiv.org/abs/1105.4108v1">v1</a>), last revised 6 Mar 2012 (this version, v2) | A few corrections, final version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph); Differential Geometry (math.DG) | https://doi.org/10.48550/arXiv.1105.4108 | We look into a construction of principal abelian varieties attached to certain spin manifolds, due to Witten and Moore-Witten around 2000 and try to place it in a broader framework. This is related to Weil intermediate Jacobians but it also suggests to associate abelian varieties to polarized even weight Hodge structur... | math-31-part-1.zip/1105.4108.pdf |
1001.0114 | Topological properties of punctual Hilbert schemes of almost-complex fourfolds (I) | [
"Julien Grivaux"
] | 31 Dec 2009 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.1001.0114 | In this article, we study topological properties of Voisin's punctual Hilbert schemes of an almost-complex fourfold $X$. In this setting, we compute their Betti numbers and construct Nakajima operators. We also define tautological bundles associated with any complex bundle on $X$, which are shown to be canonical in... | math-31-part-1.zip/1001.0114.pdf | |
2410.05110 | On the Supersingular Locus of the $\mathrm{GU}(2,n-2)$ Shimura Variety | [
"Ryosuke Shimada"
] | 7 Oct 2024 (<a href="https://arxiv.org/abs/2410.05110v1">v1</a>), last revised 29 Oct 2024 (this version, v2) | 31 pages. Minor errors corrected | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2410.05110 | We study the supersingular locus of a reduction at an inert prime of the Shimura variety attached to $\mathrm{GU}(2,n-2)$. More concretely, we decompose the supersingular locus into a disjoint union of iterated fibrations over (classical) Deligne-Lusztig varieties after taking perfection. | math-33-part-2.zip/2410.05110.pdf |
1511.02598 | Rational curves of degree four with two inner Galois points | [
"Satoru Fukasawa"
] | 9 Nov 2015 | 8 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1511.02598 | We characterize plane rational curves of degree four with two or more inner Galois points. A computer verifies the existence of plane rational curves of degree four with three inner Galois points. This would be the first example of a curve with exactly three them. Our result implies that Miura's bound is sharp for ... | math-32-part-1.zip/1511.02598.pdf |
1604.04828 | On minimal 3-folds of general type with maximal pluricanonical section index | [
"Meng Chen"
] | 17 Apr 2016 (<a href="https://arxiv.org/abs/1604.04828v1">v1</a>), last revised 5 Jun 2017 (this version, v2) | To appear in The Asian Journal of Mathematics (Special issue for Ngaiming Mok's sixtieth birthday) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1604.04828 | Let $X$ be a minimal projective 3-fold of general type. The pluricanonical section index $\delta(X)$ is defined to be the minimal integer $m$ so that $P_{m}(X)\geq 2$. According to Chen-Chen, one has either $1\leq \delta(X)\leq 15$ or $\delta(X)=18$. This note aims to intensively study those with maximal such index. A ... | math-32-part-1.zip/1604.04828.pdf |
math/9911105 | Families of hyperkähler manifolds | [
"K. Oguiso"
] | 15 Nov 1999 | 16 pages, AMSTeX | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/9911105 | We show the density of the jumping loci of the Picard number of a hyperkähler manifold under small deformation and provide several applications. In particular, we apply this to reveal the structure of hierarchy among all the narrow Mordell-Weil lattices of Jacobian K3 surfaces. | math-34-part-2.zip/math_9911105.pdf |
1811.11227 | Special cycles on the basic locus of unitary Shimura varieties at ramified primes | [
"Yousheng Shi"
] | 27 Nov 2018 (<a href="https://arxiv.org/abs/1811.11227v1">v1</a>), last revised 7 Sep 2022 (this version, v4) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1811.11227 | In this paper, we study special cycles on the basic locus of certain unitary Shimura varieties over the ramified primes and their local analogues on the corresponding Rapoport-Zink spaces. We study the support and compute the dimension of these cycles. | math-32-part-2.zip/1811.11227.pdf | |
1511.02206 | Lower Bounds for Enumerative Counts of Positive-Genus Real Curves | [
"Jingchen Niu",
"Aleksey Zinger"
] | 6 Nov 2015 | 49 pages, 3 figures, 2 tables | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.1511.02206 | We transform the positive-genus real Gromov-Witten invariants of many real-orientable symplectic threefolds into signed counts of curves. These integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints. We conclude with some implications and rela... | math-32-part-1.zip/1511.02206.pdf |
1502.01141 | Orientability for gauge theories on Calabi-Yau manifolds | [
"Yalong Cao",
"Naichung Conan Leung"
] | 4 Feb 2015 (<a href="https://arxiv.org/abs/1502.01141v1">v1</a>), last revised 18 Jun 2015 (this version, v2) | v2: 14 pages, substantially revised and expanded | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph); Differential Geometry (math.DG); Geometric Topology (math.GT) | https://doi.org/10.48550/arXiv.1502.01141 | We study orientability issues of moduli spaces from gauge theories on Calabi-Yau manifolds. Our results generalize and strengthen those for Donaldson-Thomas theory on Calabi-Yau manifolds of dimensions 3 and 4. We also prove a corresponding result in the relative situation which is relevant to the gluing problem in DT ... | math-32-part-1.zip/1502.01141.pdf |
math/9912102 | A duality for Spin Verlinde spaces and Prym theta functions | [
"C. Pauly",
"S. Ramanan"
] | 13 Dec 1999 | 18 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/9912102 | We prove canonical isomorphisms between Spin Verlinde spaces, i.e, spaces of global sections of a determinant line bundle over the moduli space of semistable Spin-bundles over a smooth projective curve C, and the dual spaces of theta functions over Prym varieties of unramified double covers of C. | math-34-part-2.zip/math_9912102.pdf |
2508.09414 | Algebraic hyperbolicity of adjoint linear systems on spherical varieties | [
"Minseong Kwon",
"Haesong Seo"
] | 13 Aug 2025 | 13 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2508.09414 | Moraga and Yeong conjectured that for a smooth complex projective variety $X$ of dimension $n$, an ample line bundle $A$ on $X$ and an integer $m \ge 3 n + 1$, very general elements of the adjoint linear system $|\omega_{X} \otimes A^{\otimes m}|$ are algebraically hyperbolic. We prove the conjecture for spherical vari... | math-34-part-1.zip/2508.09414.pdf |
1408.6978 | On the Blow-analytic Equivalence of Tribranched Plane Curves | [
"Cristina Valle"
] | 29 Aug 2014 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1408.6978 | We prove the finiteness of the number of blow-analytic equivalence classes of embedded plane curve germs for any fixed number of branches and for any fixed value of $\mu'$ ---a combinatorial invariant coming from the dual graphs of good resolutions of embedded plane curve singularities. In order to do so, we develo... | math-31-part-2.zip/1408.6978.pdf | |
0909.3685 | Linear Systems on Tropical Curves | [
"Christian Haase",
"Gregg Musiker",
"Josephine Yu"
] | 21 Sep 2009 | 28 pages, 17 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.0909.3685 | A tropical curve \Gamma is a metric graph with possibly unbounded edges, and tropical rational functions are continuous piecewise linear functions with integer slopes. We define the complete linear system |D| of a divisor D on a tropical curve \Gamma analogously to the classical counterpart. We investigate the structur... | math-31-part-1.zip/0909.3685.pdf |
alg-geom/9312003 | Thickening Calabi-Yau moduli spaces | [
"Ziv Ran"
] | 6 Dec 1993 | 9 pages, amstex2.1 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9312003 | We describe a kind of deformation of the anti-DeRham algebra on a Calabi-Yau manifold $X$. These are in 1-1 correspondence with the total cohomology $\oplus H^i (X, \C)$. | small_categories-00.zip/alg-geom_9312003.pdf |
2406.11765 | Canonical Filtrations of Finite-Dimensional Algebras | [
"Trevor Jones"
] | 17 Jun 2024 | 36 pages, LaTex. Comments welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Rings and Algebras (math.RA) | https://doi.org/10.48550/arXiv.2406.11765 | We study canonical filtrations of finite-dimensional associative algebras and Lie algebras. These filtrations are defined via optimal destabilizing one-parameter subgroups in the sense of geometric invariant theory (GIT), and appear to be a new invariant of finite-dimensional algebras. We establish some fundamental pro... | math-33-part-2.zip/2406.11765.pdf |
math/0206170 | The Kobayashi pseudometric on algebraic manifold and a canonical fibration | [
"Steven Shin-Yi Lu"
] | 18 Jun 2002 (<a href="https://arxiv.org/abs/math/0206170v1">v1</a>), last revised 8 Sep 2002 (this version, v2) | 8 pages conference proceedings. The author acknowleges the error of including the heading of the conference proceeding as given by the Proceeding's format in the previous version submitted to the archiv server during the process of the said proceedings. That heading has been eliminated from the new version and the ... | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0206170 | Given a compact complex manifold X of dimension n, we define a bimeromorphic invariant $\kappa_+(X)$ as the maximum p for which there is a saturated line subsheaf L of the sheaf of holomorphic p forms whose Kodaira dimension $\kappa (L)$ equals p. We call X special if $\kappa_+(X)=0$. We give some evidence that this co... | math-34-part-1.zip/math_0206170.pdf |
math/0111094 | The Continuous Hochschild Cochain Complex of a Scheme | [
"Amnon Yekutieli"
] | 8 Nov 2001 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC); K-Theory and Homology (math.KT) | https://doi.org/10.48550/arXiv.math/0111094 | Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we assign the complex Hom^{cont}_X(C(X),M) of continuous Hochschild cochains with valu... | math-34-part-1.zip/math_0111094.pdf | |
2112.13298 | The behavior of essential dimension under specialization II | [
"Zinovy Reichstein",
"Federico Scavia"
] | 25 Dec 2021 | Sequel to The behavior of essential dimension under specialization, can be read independently. 23 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Group Theory (math.GR) | https://doi.org/10.48550/arXiv.2112.13298 | Let $G$ be a linear algebraic group over a field. We show that, under mild assumptions, in a family of primitive generically free $G$-varieties over a base variety $B$ the essential dimension of the geometric fibers may drop on a countable union of Zariski closed subsets of $B$ and stays constant away from this countab... | math-33-part-1.zip/2112.13298.pdf |
2312.16808 | On double Danielewski varieties | [
"Xiaosong Sun",
"Shuai Zeng"
] | 28 Dec 2023 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.2312.16808 | In this paper, we study the double Danielewski varieties which arose from the research on the classical Cancellation Problem. We describe the Makar-Limanov invariant and locally nilpotent derivations of these varieties. And in a subsequent paper we will describe the automorphisms groups of the varieties and verify that... | math-33-part-2.zip/2312.16808.pdf | |
1404.3373 | Wilder McKay correspondences | [
"Takehiko Yasuda"
] | 13 Apr 2014 (<a href="https://arxiv.org/abs/1404.3373v1">v1</a>), last revised 5 Jun 2014 (this version, v3) | 42 pages. The title has been changed from the previous "The motivic McKay correspondence for non-linear actions on possibly singular spaces". A new added subject is computations of weight functions and masses for some non-permutation representations. Comments are welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1404.3373 | A conjectural generalization of the McKay correspondence in terms of stringy invariants to arbitrary characteristic, including the wild case, was recently formulated by the author in the case where the given finite group linearly acts on an affine space. In cases of very special groups and representations, the conjectu... | math-31-part-2.zip/1404.3373.pdf |
math/0103204 | Deforming curves in jacobians to non-jacobians I: curves in $C^{(2)}$ | [
"E. Izadi"
] | 29 Mar 2001 (<a href="https://arxiv.org/abs/math/0103204v1">v1</a>), last revised 21 Jun 2005 (this version, v3) | amslatex, 25 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0103204 | We introduce deformation theoretic methods for determining when a curve $X$ in a non-hyperelliptic jacobian $JC$ will deform with $JC$ to a non-jacobian. We apply these methods to a particular class of curves in the second symmetric power $C^{(2)}$ of $C$. More precisely, given a pencil $g^1_d$ of degree $d$ on $C$, le... | math-34-part-1.zip/math_0103204.pdf |
2503.24339 | A family of indecomposable rank-$n$ vector bundles on $\mathbb P^n\times\mathbb P^n$ in positive characteristics | [
"Ziv Ran",
"Jürgen Rathmann"
] | 31 Mar 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2503.24339 | We construct a sequence of rank-$n$ indecomposable vector bundles on $\mathbb P^n\times\mathbb P^n$ for every $n\geq 2$ and in every positive characteristic that are not pullbacks via any map $\mathbb P^n\times\mathbb P^n\to \mathbb P^{m} $ | math-33-part-2.zip/2503.24339.pdf | |
2404.09102 | Notes on Nash modification | [
"A. Nobile"
] | 13 Apr 2024 | 19 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2404.09102 | The Nash blowing-up (or modification) of an algebraic variety $X$ is a canonical process that produces a proper, birational morphism $\pi : X' \to X$ of varieties. It is expected that the singularities of $X'$ will be better than those of $X$. In the mid-1970's, it was proved that in characteristic zero, ${... | math-33-part-2.zip/2404.09102.pdf |
2410.16113 | Flips and Flops Constructed by GIT Quotient | [
"Hung-Pin Chang"
] | 21 Oct 2024 (<a href="https://arxiv.org/abs/2410.16113v1">v1</a>), last revised 12 Dec 2024 (this version, v2) | 23 pages, 1 figure, 7 tables. Updated references to acknowledge the independent work of Laura Mallinson in her 2022 Ph.D. thesis, as pointed out by Professor Gavin Brown. Comments are welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2410.16113 | Brown constructed a series of threefold flips given by the GIT quotient of a hypersurface in $\mathbb{C}^5$. In this article, we classify threefold flips and flops which are the GIT quotients of complete intersections in $\mathbb{C}^6$. We also show that there are no more new examples as GIT quotients of complete inter... | math-33-part-2.zip/2410.16113.pdf |
2312.02842 | GIT stability of divisors in products of projective spaces | [
"Ioannis Karagiorgis",
"Theresa A. Ortscheidt",
"Theodoros S. Papazachariou"
] | 5 Dec 2023 (<a href="https://arxiv.org/abs/2312.02842v1">v1</a>), last revised 6 Dec 2023 (this version, v2) | v2: Added references and corrected figures. Comments very welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2312.02842 | We study GIT stability of divisors in products of projective spaces. We first construct a finite set of one-parameter subgroups sufficient to determine the stability of the GIT quotient. In addition, we characterise all maximal orbits of not stable and strictly semistable pairs, as well as minimal closed orbits of stri... | math-33-part-2.zip/2312.02842.pdf |
1906.07044 | Derived Non-archimedean analytic Hilbert space | [
"Jorge António",
"Mauro Porta"
] | 17 Jun 2019 | 28 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1906.07044 | In this short paper we combine the representability theorem introduced in [17, 18] with the theory of derived formal models introduced in [2] to prove the existence representability of the derived Hilbert space RHilb(X) for a separated k-analytic space X. Such representability results relies on a localization theorem s... | math-32-part-2.zip/1906.07044.pdf |
0907.4170 | On existence of log minimal models II | [
"Caucher Birkar"
] | 23 Jul 2009 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0907.4170 | We prove that the existence of log minimal models in dimension $d$ essentially implies the LMMP with scaling in dimension $d$. As a consequence we prove that a weak nonvanishing conjecture in dimension $d$ implies the minimal model conjecture in dimension $d$. | math-31-part-1.zip/0907.4170.pdf | |
math/0608020 | A volume maximizing canonical surface in 3-space | [
"Ingrid Bauer",
"Fabrizio Catanese"
] | 1 Aug 2006 | 14 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.math/0608020 | Answering a question posed by Enriques, we construct a minimal smooth algebraic surface $S$ of general type over the complex numbers with $K^2 = 45$ and $p_g = 4$, and with birational canonical map. Our surface is a regular (q=0) ball quotient which is an etale quotient of a Hirzebruch covering of the plane. The canoni... | math-34-part-1.zip/math_0608020.pdf |
1910.07984 | Deformations of the tangent bundle of projective manifolds | [
"Thomas Peternell"
] | 17 Oct 2019 (<a href="https://arxiv.org/abs/1910.07984v1">v1</a>), last revised 17 Jul 2020 (this version, v2) | Final version, 34 pages, to appear in International Journal of Mathematics | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1910.07984 | We investigate when the tangent bundle of a projective manifold has a non-trivial first order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space. | math-32-part-2.zip/1910.07984.pdf |
1010.2709 | [
"Yoav Yaffe"
] | 13 Oct 2010 (<a href="https://arxiv.org/abs/1010.2709v1">v1</a>), last revised 21 Oct 2010 (this version, v3) | This paper has been withdrawn by the author, Noa Lavi, due to a mistake | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Logic (math.LO) | https://doi.org/10.48550/arXiv.1010.2709 | Version 1 of this paper (<a href="https://arxiv.org/abs/1010.2709v1" data-arxiv-id="1010.2709v1" class="link-https">arXiv:1010.2709v1</a>) was submitted exclusively by Noa Lavi, without prior knowledge, let alone consent, by Yoav Yaffe. Yoav Yaffe is {\em not} an author of any version of this paper, with the exception ... | math-31-part-1.zip/1010.2709.pdf | |
math/9902017 | The moduli space of (1,11)-polarized abelian surfaces is unirational | [
"Mark Gross",
"Sorin Popescu"
] | 2 Feb 1999 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/9902017 | We prove that the moduli space A_{11}^{lev} of (1,11) polarized abelian surfaces with level structure of canonical type is birational to Klein's cubic hypersurface: <br>a^2b+b^2c+c^2d+d^2e+e^2a=0 in P^4. <br>Therefore, A_{11}^{lev} is unirational but not rational, and there are no Gamma_{11}-cusp forms of weight 3.... | math-34-part-2.zip/math_9902017.pdf | |
2502.11704 | Motivic counting of rational curves with tangency conditions via universal torsors | [
"Loïs Faisant"
] | 17 Feb 2025 | 37 pages, comments welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2502.11704 | Using the formalism of Cox rings and universal torsors, we prove a decomposition of the Grothendieck motive of the moduli space of morphisms from an arbitrary smooth projective curve to a Mori Dream Space (MDS). <br>For the simplest cases of MDS, that of toric varieties, we use this decomposition to prove an instance o... | math-33-part-2.zip/2502.11704.pdf |
math/0304223 | Submanifolds with splitting tangent sequence | [
"Priska Jahnke"
] | 16 Apr 2003 (<a href="https://arxiv.org/abs/math/0304223v1">v1</a>), last revised 20 Dec 2004 (this version, v3) | 15 pages, LaTeX2e; Proposition 5.4. changed, proof of Theorem 6.3. modified; final version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0304223 | In the late 50's A. Van de Ven stated that the only compact submanifolds with splitting tangent sequence of the projective space are linear subspaces. In this paper a classification of all submanifolds with splitting tangent sequence of some further classes of (homogeneous) manifolds is given, like quadrics or abel... | math-34-part-1.zip/math_0304223.pdf |
2201.12588 | Orbits on K3 Surfaces of Markoff Type | [
"Elena Fuchs",
"Matthew Litman",
"Joseph H. Silverman",
"Austin Tran"
] | 29 Jan 2022 (<a href="https://arxiv.org/abs/2201.12588v1">v1</a>), last revised 15 Sep 2022 (this version, v2) | 55 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Dynamical Systems (math.DS); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2201.12588 | Let $\mathcal{W}\subset\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$ be a surface given by the vanishing of a $(2,2,2)$-form. These surfaces admit three involutions coming from the three projections $\mathcal{W}\to\mathbb{P}^1\times\mathbb{P}^1$, so we call them $\textit{tri-involutive K3 (TIK3) surfaces}$. By anal... | math-33-part-1.zip/2201.12588.pdf |
2005.02202 | Some Quot schemes in tilted hearts and moduli spaces of stable pairs | [
"Franco Rota"
] | 5 May 2020 (<a href="https://arxiv.org/abs/2005.02202v1">v1</a>), last revised 20 Oct 2021 (this version, v3) | 27 pages, 1 figure. Subsumes results from Chapter 2 of the author's PhD thesis. V2: References updated. V3: final version, to appear in Internat. J. Math. Comments are welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2005.02202 | For a smooth projective variety $X$, we study analogs of Quot functors in hearts of non-standard $t$-structures of $D^b(\mathrm{Coh}(X))$. The technical framework is that of families of $t$-structures, as studied in <a href="https://arxiv.org/abs/1902.08184" data-arxiv-id="1902.08184" class="link-https">arXiv:1902.0818... | math-32-part-2.zip/2005.02202.pdf |
1510.07277 | Hurwitz correspondences on compactifications of $\mathcal{M}_{0,N}$ | [
"Rohini Ramadas"
] | 25 Oct 2015 (<a href="https://arxiv.org/abs/1510.07277v1">v1</a>), last revised 5 May 2016 (this version, v2) | 30 pages, major revisions - result strengthened, new introduction, submitted | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1510.07277 | Hurwitz correspondences are certain multivalued self-maps of the moduli space $\mathcal{M}_{0,N}$. They arise in the study of Thurston's topological characterization of rational functions. We consider the dynamics of Hurwitz correspondences and ask: On which compactifications of $\mathcal{M}_{0,N}$ should they be s... | math-32-part-1.zip/1510.07277.pdf |
1712.05716 | On injective endomorphisms of symbolic schemes | [
"Tullio Ceccherini-Silberstein",
"Michel Coornaert",
"Xuan Kien Phung"
] | 15 Dec 2017 (<a href="https://arxiv.org/abs/1712.05716v1">v1</a>), last revised 6 Jul 2018 (this version, v3) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Dynamical Systems (math.DS); Group Theory (math.GR) | https://doi.org/10.48550/arXiv.1712.05716 | Building on the seminal work of Gromov on endomorphisms of symbolic algebraic varieties [10], we introduce a notion of cellular automata over schemes which generalize affine algebraic cellular automata in [7]. We extend known results to this more general setting. We also establish several new ones regarding the closed ... | math-32-part-2.zip/1712.05716.pdf | |
1111.5324 | Differential equations as embedding obstructions and vanishing theorems | [
"Damian Brotbek"
] | 22 Nov 2011 | 11 page, comments are welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1111.5324 | We generalize a vanishing theorem for the cohomology of symmetric powers of the cotangent bundle of subvarieties of projective space due to Schneider. From this we deduce new vanishing results for Green-Griffiths jet differential bundles, generalizing results of Diverio and Pacienza-Rousseau. | math-31-part-2.zip/1111.5324.pdf |
1206.0438 | Moduli of products of stable varieties | [
"Bhargav Bhatt",
"Wei Ho",
"Zsolt Patakfalvi",
"Christian Schnell"
] | 3 Jun 2012 | 26 pages, suggestions and comments are welcomed | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1206.0438 | We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined morphism from the product of moduli spaces of stable varieties to the moduli space of a product of stable varieties, (b) ... | math-31-part-2.zip/1206.0438.pdf |
alg-geom/9410027 | Submodules of the deficiency modules and an extension of Dubreil's Theorem | [
"Heath Martin",
"Juan Migliore"
] | 26 Oct 1994 | 18 pages, LaTeX, version 2.09 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9410027 | In its most basic form, Dubreil's Theorem states that for an ideal $I$ defining a codimension $2$, arithmetically Cohen--Macaulay subscheme of projective $n$-space, the number of generators of $I$ is bounded above by the minimal degree of a minimal generator plus $1$. By introducing a new ideal $J$ which is the com... | small_categories-00.zip/alg-geom_9410027.pdf |
1312.0338 | Non-Archimedean analytic geometry as relative algebraic geometry | [
"Oren Ben-Bassat",
"Kobi Kremnizer"
] | 2 Dec 2013 (<a href="https://arxiv.org/abs/1312.0338v1">v1</a>), last revised 6 Aug 2015 (this version, v3) | added material on quasi-coherent modules, connection to derived analytic geometry, corrected mistakes | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Category Theory (math.CT); Functional Analysis (math.FA); Number Theory (math.NT); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1312.0338 | We show that Berkovich analytic geometry can be viewed as relative algebraic geometry in the sense of Toën--Vaquié--Vezzosi over the category of non-Archimedean Banach spaces. For any closed symmetric monoidal quasi-abelian category we can define a topology on certain subcategories of the of the category of affine sche... | math-31-part-2.zip/1312.0338.pdf |
1211.3945 | Some fourth order CY-type operators with non symplectically rigid monodromy | [
"Michael Bogner",
"Stefan Reiter"
] | 16 Nov 2012 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Classical Analysis and ODEs (math.CA) | https://doi.org/10.48550/arXiv.1211.3945 | We study tuples of matrices with rigidity index two in $\Sp_4(\mathbb{C})$, which are potentially induced by differential operators of Calabi-Yau type. The constructions of those monodromy tuples via algebraic operations and middle convolutions and the related constructions on the level differential operators lead to p... | math-31-part-2.zip/1211.3945.pdf | |
1806.05704 | Ansatz for $(-1)^{n-1}\nabla p_n$ | [
"Soumya Dipta Banerjee",
"Mahir Bilen Can",
"Adriano Garsia"
] | 14 Jun 2018 (<a href="https://arxiv.org/abs/1806.05704v1">v1</a>), last revised 16 Aug 2018 (this version, v2) | A mistake is fixed | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.1806.05704 | We construct a special family of equivariant coherent sheaves on the Hilbert scheme on $n$-points in the affine plane. The equivariant Euler characteristic of these sheaves are closely related to the symmetic functions $(-1)^{n-1} \nabla p_n$. We prove a higher cohomology vanishing result of these sheaves. It follows f... | math-32-part-2.zip/1806.05704.pdf |
math/0304162 | Multihomogeneous resultant formulae by means of complexes | [
"A. Dickenstein",
"I. Emiris"
] | 13 Apr 2003 | 30 pages. To appear: Journal of Symbolic Computation | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.math/0304162 | We provide conditions and algorithmic tools so as to classify and construct the smallest possible determinantal formulae for multihomogeneous resultants arising from Weyman complexes associated to line bundles in products of projective spaces. We also examine the smallest Sylvester-type matrices, generically of full ra... | math-34-part-1.zip/math_0304162.pdf |
1912.12536 | Modular functions and resolvent problems | [
"Benson Farb",
"Mark Kisin",
"Jesse Wolfson. Appendix by Nate Harman"
] | 28 Dec 2019 | 33 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1912.12536 | The link between modular functions and algebraic functions was a driving force behind the 19th century study of both. Examples include the solutions by Hermite and Klein of the quintic via elliptic modular functions and the general sextic via level $2$ hyperelliptic functions. This paper aims to apply modern arithmetic... | math-32-part-2.zip/1912.12536.pdf |
1307.6514 | Short Tops and Semistable Degenerations | [
"Ryan Davis",
"Charles Doran",
"Adam Gewiss",
"Andrey Novoseltsev",
"Dmitri Skjorshammer",
"Alexa Syryczuk",
"Ursula Whitcher"
] | 24 Jul 2013 (<a href="https://arxiv.org/abs/1307.6514v1">v1</a>), last revised 9 Jun 2014 (this version, v3) | 18 pages, 7 figures. Improved description of Algorithm 3.3. This version will appear in the Journal of Experimental Mathematics | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.1307.6514 | One may construct a large class of Calabi-Yau varieties by taking anticanonical hypersurfaces in toric varieties obtained from reflexive polytopes. If the intersection of a reflexive polytope with a hyperplane through the origin yields a lower-dimensional reflexive polytope, then the corresponding Calabi-Yau varieties ... | math-31-part-2.zip/1307.6514.pdf |
1204.6254 | On the Göttsche Threshold | [
"Steven L. Kleiman",
"Vivek V. Shende",
"with an appendix by Ilya Tyomkin"
] | 27 Apr 2012 (<a href="https://arxiv.org/abs/1204.6254v1">v1</a>), last revised 6 Feb 2013 (this version, v2) | 20 pages, final version, to appear in the Harris60 Volume of the Clay series (put out by the American Mathematical Society) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1204.6254 | For a line bundle L on a smooth surface S, it is now known that the degree of the Severi variety of cogenus-d curves is given by a universal polynomial in the Chern classes of L and S if L is d-very ample. For S rational, we relax the latter condition substantially: it suffices that three key loci be of codimension mor... | math-31-part-2.zip/1204.6254.pdf |
math/0112086 | Families of supersingular curves in characteristic 2 | [
"Jasper Scholten",
"Hui June Zhu"
] | 9 Dec 2001 | 11 pages, LaTeX | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.math/0112086 | This paper determines the normal forms of hyperelliptic supersingular curves of genus g over an algebraically closed field F of characteristic 2 for 0 < g< 9. We also show that every hyperelliptic supersingular curve of genus 9 over F has an equation y^2-y=x^19+c^8x^9+c^3x for some c in F_2bar. The paper determin... | math-34-part-1.zip/math_0112086.pdf |
alg-geom/9212003 | The enumeration of simultaneous higher-order contacts between plane curves | [
"Susan Jane Colley",
"Gary Kennedy"
] | 8 Dec 1992 (<a href="https://arxiv.org/abs/alg-geom/9212003v1">v1</a>), last revised 30 Jun 1993 (this version, v2) | 32 pages, AmS-TeX v2.1 (Revised statement and proof of one lemma; other minor changes.) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9212003 | Using the Semple bundle construction, we derive an intersection-theoretic formula for the number of simultaneous contacts of specified orders between members of a generic family of degree $d$ plane curves and finitely many fixed curves. The contacts counted by the formula occur at nonsingular points of both the members... | small_categories-00.zip/alg-geom_9212003.pdf |
2501.18551 | Finite subgroups of maximal order of the Cremona group over the rationals | [
"Ahmed Abouelsaad"
] | 30 Jan 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2501.18551 | Let $\Cr_\Q(2)$ be the Cremona group of rank $2$ over rational numbers. We give a classification of large finite subgroups $G$ of $\Cr_\Q(2)$ and give a new sharp bound smaller (but not multiplicative) than $M(\Q)=120960 = 2^7\cdot3^3\cdot5\cdot7$; the one given in \cite{MR2567402}. In particular, we prove that any fin... | math-33-part-2.zip/2501.18551.pdf | |
1107.5331 | $sl_2$ conformal block divisors and the nef cone of $\bar{M}_{0,n}$ | [
"David Swinarski"
] | 26 Jul 2011 | 16 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1107.5331 | We show that $sl_2$ conformal block divisors do not cover the nef cone of $\bar{M}_{0,6}$, or the $S_9$-invariant nef cone of $\bar{M}_{0,9}$. A key point is to relate the nonvanishing of intersection numbers between these divisors and F-curves to the nonemptiness of some explicitly defined polytopes. Several experimen... | math-31-part-1.zip/1107.5331.pdf |
2305.13763 | Relative connections on Principal bundles and relative equivariant structures | [
"Mainak Poddar",
"Anoop Singh"
] | 23 May 2023 | 17 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2305.13763 | We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over a complex analytic family. We also introduce the notion of relative equivariant ... | math-33-part-2.zip/2305.13763.pdf |
1904.11222 | The fundamental group of partial compactifications of the complement of a real line arrangement | [
"Rodolfo Aguilar"
] | 25 Apr 2019 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1904.11222 | Let $\mathscr{A}$ be a real projective line arrangement and $M(\mathscr{A})$ its complement in $\mathbb{CP}^2$. We obtain an explicit expression in terms of Randell's generators of the meridians around the exceptional divisors in the blow-up $\bar{X}$ of $\mathbb{CP}^2$ in the singular points of $\mathscr{A}$. We u... | math-32-part-2.zip/1904.11222.pdf | |
1509.04993 | Counterexamples of Kodaira vanishing for smooth surfaces of general type in positive characteristic | [
"Xudong Zheng"
] | 16 Sep 2015 | 13 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1509.04993 | We generalize the construction of Raynaud of smooth projective surfaces of general type in positive characteristic that violate the Kodaira vanishing theorem. This corrects an earlier paper of the same purpose. These examples are smooth surfaces fibered over a smooth curve whose direct images of the relative dualizing ... | math-32-part-1.zip/1509.04993.pdf |
2407.14488 | Perfectoidness via Sen Theory and Applications to Shimura Varieties | [
"Tongmu He"
] | 19 Jul 2024 (<a href="https://arxiv.org/abs/2407.14488v1">v1</a>), last revised 23 Jul 2025 (this version, v2) | 59 pages, to appear in J. Amer. Math. Soc | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2407.14488 | Sen's theorem on the ramification of a $p$-adic analytic Galois extension of $p$-adic local fields shows that its perfectoidness is equivalent to the non-vanishing of its arithmetic Sen operator. By developing $p$-adic Hodge theory for general valuation rings, we establish a geometric analogue of Sen's criterio... | math-33-part-2.zip/2407.14488.pdf |
1706.05244 | Differential forms in positive characteristic II: cdh-descent via functorial Riemann-Zariski spaces | [
"Annette Huber",
"Shane Kelly"
] | 16 Jun 2017 | 37 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1706.05244 | This paper continues our study of the sheaf associated to Kähler differentials in the cdh-topology and its cousins, in positive characteristic, without assuming resolution of singularities. The picture for the sheaves themselves is now fairly complete. We give a calculation $\mathcal{O}_{cdh}(X) \cong \mathcal{O}(X^{sn... | math-32-part-1.zip/1706.05244.pdf |
2205.13318 | On the slope inequalities for extremal curves | [
"Valentina Beorchia",
"Michela Brundu"
] | 26 May 2022 | 21 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2205.13318 | The present paper concerns the question of the violation of the r-th inequality for extremal curves in the projective r-space, posed by T. Kato and G. Martens. We show that the answer is negative in many cases. The result is obtained by a detailed analysis of the geometry of extremal curves and their canonical model. A... | math-33-part-1.zip/2205.13318.pdf |
1011.2965 | Weakly uniform rank two vector bundles on multiprojective spaces | [
"Edoardo Ballico",
"Francesco Malaspina"
] | 12 Nov 2010 | 6 pages no figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1011.2965 | Here we classify the weakly uniform rank two vector bundles on multiprojective spaces. Moreover we show that every rank $r>2$ weakly uniform vector bundle with splitting type $a_{1,1}=...=a_{r,s}=0$ is trivial and every rank $r>2$ uniform vector bundle with splitting type $a_1>...>a_r$, splits. | math-31-part-1.zip/1011.2965.pdf |
1309.0075 | Note on affine Deligne-Lusztig varieties | [
"Xuhua He"
] | 31 Aug 2013 | 10 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1309.0075 | This note is based on my talk at ICCM 2013, Taipei. We give an exposition of the group-theoretic method and recent results on the questions of non-emptiness and dimension of affine Deligne-Lusztig varieties in affine flag varieties. | math-31-part-2.zip/1309.0075.pdf |
1805.05413 | On the integrality of Seshadri constants of abelian surfaces | [
"Thomas Bauer",
"Felix Fritz Grimm",
"Maximilian Schmidt"
] | 14 May 2018 (<a href="https://arxiv.org/abs/1805.05413v1">v1</a>), last revised 24 Sep 2019 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1805.05413 | In this paper we consider the question of when Seshadri constants on abelian surfaces are integers. Our first result concerns self-products $E\times E$ of elliptic curves: If $E$ has complex multiplication in $\Z[i]$ or in $\Z[\frac12(1+i\sqrt3)]$ or if $E$ has no complex multiplication at all, then it is known that fo... | math-32-part-2.zip/1805.05413.pdf | |
0712.1576 | A simple proof for the existence of Zariski decompositions on surfaces | [
"Thomas Bauer"
] | 10 Dec 2007 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0712.1576 | In this note we give a quick and simple proof of the existence (and uniqueness) of Zariski decompositions on surfaces. While Zariski's original proof employs a rather sophisticated procedure to construct the negative part of the decomposition, the present approach is based on the idea that the positive part can be ... | math-31-part-1.zip/0712.1576.pdf | |
1707.03773 | Frobenius splitting of thick flag manifolds of Kac-Moody algebras | [
"Syu Kato"
] | 12 Jul 2017 (<a href="https://arxiv.org/abs/1707.03773v1">v1</a>), last revised 10 Jun 2018 (this version, v2) | 20pages; v2 major revision. Overall improvement and corrections | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1707.03773 | We explain that the Plücker relations provide the defining equations of the thick flag manifold associated to a Kac-Moody algebra. This naturally transplant the result of Kumar-Mathieu-Schwede about the Frobenius splitting of thin flag manifolds to the thick case. As a consequence, we provide a description of the globa... | math-32-part-1.zip/1707.03773.pdf |
1111.0196 | Stability of tangent bundle on the moduli space of stable bundles on a curve | [
"Jaya N. N. Iyer"
] | 1 Nov 2011 (<a href="https://arxiv.org/abs/1111.0196v1">v1</a>), last revised 12 Feb 2014 (this version, v5) | Revised version, Lemma 4.3,4.4 added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Differential Geometry (math.DG) | https://doi.org/10.48550/arXiv.1111.0196 | In this paper, we prove that the tangent bundle of the moduli space $\cSU_C(r,d)$ of stable bundles of rank $r>2$ and of fixed determinant of degree $d$ (such that $(r,d)=1$), on a smooth projective curve $C$ is always stable, in the sense of Mumford-Takemoto. This verifies a well-known conjecture, and is related to... | math-31-part-2.zip/1111.0196.pdf |
2007.01849 | Effective birationality for sub-pairs with real coefficients | [
"Jingjun Han",
"Jihao Liu"
] | 3 Jul 2020 | 21 pages, comments are welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2007.01849 | For $\epsilon$-lc Fano type varieties $X$ of dimension $d$ and a given finite set $\Gamma$, we show that there exists a positive integer $m_0$ which only depends on $\epsilon,d$ and $\Gamma$, such that both $|-mK_X-\sum_i\lceil mb_i\rceil B_i|$ and $|-mK_X-\sum_i\lfloor mb_i\rfloor B_i|$ define birational maps for any ... | math-33-part-1.zip/2007.01849.pdf |
2302.00555 | On torus quotients of Schubert varieties in orthogonal Grassmannian-II | [
"Arpita Nayek",
"Pinakinath Saha"
] | 1 Feb 2023 | 19 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.2302.00555 | Let $G=SO(8n+4,\mathbb{C})$ ($n\ge 1$). Let $B$ be a Borel subgroup of $G$ containing a maximal torus $T$ of $G.$ Let $P (\supset B)$ denote the maximal parabolic subgroup of $G$ corresponding to the simple root $\alpha_{4n+2}$. In this article, we prove projective normality of the GIT quotients of certain Schubert var... | math-33-part-1.zip/2302.00555.pdf |
1001.0435 | On Donaldson-Thomas invariants of threefold stacks and gerbes | [
"Amin Gholampour",
"Hsian-Hua Tseng"
] | 4 Jan 2010 | 13 pages, Preliminary version, comments are welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1001.0435 | We present a construction of Donaldson-Thomas invariants for three-dimensional projective Calabi-Yau Deligne-Mumford stacks. We also study the structure of these invariants for etale gerbes over such stacks. | math-31-part-1.zip/1001.0435.pdf |
2502.16009 | Asymptotic Dynamics on Character Varieties over Finite Fields | [
"Cigole Thomas"
] | 21 Feb 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2502.16009 | In this paper, we prove the lack of asymptotic transitivity of the outer automorphism group action of $\mathbb{Z}^r$ on $\mathrm{SL}_n(\mathbb{F}_q)$-character varieties of $\mathbb{Z}^r$ for $n=2,3$ and $r\geq 2$. Along the way, we stratify the character varieties and compute the $E$-polynomial, also known as the Hodg... | math-33-part-2.zip/2502.16009.pdf | |
2501.08264 | Lipschitz Geometry of Mixed Pham-Brieskorn Singularities | [
"Inácio Rabelo"
] | 14 Jan 2025 | 15 pages, 1 figure | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2501.08264 | We give conditions for topological and bi-Lipschitz equivalences within a class of mixed singularities of Pham-Brieskorn type. We then derive the construction of topologically trivial infinite families with distinct bi-Lipschitz types. We also investigate the same problem applied to the mixed surfaces defined by these ... | math-33-part-2.zip/2501.08264.pdf |
1111.0614 | General Bezout-type theorems | [
"Pinaki Mondal"
] | 2 Nov 2011 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1111.0614 | In this sequel to arxiv:<a href="https://arxiv.org/abs/1012.0835" data-arxiv-id="1012.0835" class="link-https">arXiv:1012.0835</a> we develop Bezout type theorems for semidegrees (including an explicit formula for {\em iterated semidegrees}) and an inequality for subdegrees. In addition we prove (in case of surfaces) a... | math-31-part-2.zip/1111.0614.pdf | |
2012.09880 | On the geometry of affine Deligne-Lusztig varieties for quasi-split groups with very special leve | [
"Paul Hamacher"
] | 17 Dec 2020 | 30 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2012.09880 | In this paper we discuss the geometry of affine Deligne Lusztig varieties with very special level structure, determining their dimension and connected and irreducible components. As application, we prove the Grothendieck conjecture for Shimura varieties with very special level at $p$ and a function field analogue. | math-33-part-1.zip/2012.09880.pdf |
2307.01607 | Rational Variant of Hartogs' Theorem on Separate Holomorphicity | [
"Hanwen Liu"
] | 4 Jul 2023 (<a href="https://arxiv.org/abs/2307.01607v1">v1</a>), last revised 6 Jul 2023 (this version, v2) | 7 pages, 1 figure | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.2307.01607 | Given an uncountable algebraically closed field $K$, we proved that if partially defined function $f\colon K \times \dots \times K \dashrightarrow K$ defined on a Zariski open subset of the $n$-fold Cartesian product $K \times \dots \times K$ is rational in each coordinate whilst other coordinates are held constant, th... | math-33-part-2.zip/2307.01607.pdf |
1212.0522 | Local finite dimensional Gorenstein k-algebras having Hilbert function (1,5,5,1) are smoothable | [
"Joachim Jelisiejew"
] | 3 Dec 2012 | 4 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1212.0522 | Let k be an algebraically closed field of characteristic 0. The question of irreducibility of the punctual Hilbert scheme Hilb_d P^n and its Gorenstein locus for various d was studied in [CEVV8, CN9, CN10, CN11]. In this short paper we prove that the subschemes corresponding to the Gorenstein algebras having Hilbert fu... | math-31-part-2.zip/1212.0522.pdf |
1402.1292 | Parity and symmetry in intersection and ordinary cohomology | [
"Shenghao Sun",
"Weizhe Zheng"
] | 6 Feb 2014 (<a href="https://arxiv.org/abs/1402.1292v1">v1</a>), last revised 10 Jan 2018 (this version, v7) | 48 pages. v7: improved 4.3.1 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1402.1292 | In this paper, we show that the Galois representations provided by $\ell$-adic cohomology of proper smooth varieties, and more generally by $\ell$-adic intersection cohomology of proper varieties, over any field, are orthogonal or symplectic according to the degree. We deduce this from a preservation result of orthogon... | math-31-part-2.zip/1402.1292.pdf |
2208.01091 | Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles | [
"Wei Gu",
"Leonardo C. Mihalcea",
"Eric Sharpe",
"Hao Zou"
] | 1 Aug 2022 (<a href="https://arxiv.org/abs/2208.01091v1">v1</a>), last revised 23 Sep 2024 (this version, v3) | 39 pages; changes in this version: removed section about filtration of the QK theory ring (no longer needed); changed proofs of Thm. 8.2 and Thm. 11.12 so they now use an argument based on finiteness of certain completions (this fixed a gap in the previous version); added a reference to a finiteness criterion in Remark... | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.2208.01091 | We prove a `Whitney' presentation, and a `Coulomb branch' presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm{Gr}(k;n)$, inspired from physics, and stated in an earlier paper. The first presentation is obtained by quantum deforming the product of the Hirzebruch $\lambda_y... | math-33-part-1.zip/2208.01091.pdf |
1210.7369 | On h-principle and specialness for complex projective manifolds | [
"Frédéric Campana",
"Jörg Winkelmann"
] | 27 Oct 2012 (<a href="https://arxiv.org/abs/1210.7369v1">v1</a>), last revised 4 Nov 2012 (this version, v2) | 21 pages (minor corrections) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1210.7369 | We show that a complex projective manifold X which satisfies the Gromov's h-principle is `special', and raise some questions about the reverse implication, the extension to the quasi-K\" ahler case, and the relationships of these properties to the `Oka' property. The guiding principle is that the existe... | math-31-part-2.zip/1210.7369.pdf |
1805.05920 | Fundamental classes in motivic homotopy theory | [
"Frédéric Déglise",
"Fangzhou Jin",
"Adeel A. Khan"
] | 15 May 2018 (<a href="https://arxiv.org/abs/1805.05920v1">v1</a>), last revised 29 Jan 2021 (this version, v3) | 45 pages, final version; to appear in JEMS | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); K-Theory and Homology (math.KT) | https://doi.org/10.48550/arXiv.1805.05920 | We develop the theory of fundamental classes in the setting of motivic homotopy theory. Using this we construct, for any motivic spectrum, an associated bivariant theory in the sense of Fulton-MacPherson. We import the tools of Fulton's intersection theory into this setting: (refined) Gysin maps, specialization map... | math-32-part-2.zip/1805.05920.pdf |
2310.13651 | Cyclic covers: Hodge theory and categorical Torelli theorems | [
"Hannah Dell",
"Augustinas Jacovskis",
"Franco Rota"
] | 20 Oct 2023 (<a href="https://arxiv.org/abs/2310.13651v1">v1</a>), last revised 8 Dec 2023 (this version, v2) | 19 pages. Added a categorical Torelli theorem for prime Fano threefolds of index 2 and degree 1. Slightly weakened the generality assumptions. Other minor changes. Comments welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2310.13651 | Let $Y$ admit a rectangular Lefschetz decomposition of its derived category, and consider a cyclic cover $X\to Y$ ramified over a divisor $Z$. In a setting not considered by Kuznetsov and Perry, we define a subcategory $\mathcal{A}_Z$ of the equivariant derived category of $X$ which contains, rather than is contained i... | math-33-part-2.zip/2310.13651.pdf |
math/0405018 | Counting rational maps onto surfaces and fundamental groups | [
"T. Bandman",
"A. Libgober"
] | 2 May 2004 | 19 pages, AMSTeX | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0405018 | We consider the class of quasiprojective varieties admitting a dominant morphism onto a curve with negative Euler characteristic. The existence of such a morphism is a property of the fundamental group. We show that for a variety in this class the number of maps onto a hyperbolic curve or surfaces can be estimated in t... | math-34-part-1.zip/math_0405018.pdf |
1910.06200 | A Simple Proof of Voisin's Theorem for Canonical Curves of Even Genus | [
"Michael Kemeny"
] | 14 Oct 2019 (<a href="https://arxiv.org/abs/1910.06200v1">v1</a>), last revised 21 Oct 2019 (this version, v2) | Updated introduction, minor stylistic changes | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1910.06200 | We give a simple proof of Voisin's Theorem for general canonical curves of even genus. This completely determines the terms of the minimal free resolution of the coordinate ring of such curves. | math-32-part-2.zip/1910.06200.pdf |
1603.03929 | On the connectedness of the standard web of Calabi-Yau 3-folds and small transitions | [
"Sz-Sheng Wang"
] | 12 Mar 2016 (<a href="https://arxiv.org/abs/1603.03929v1">v1</a>), last revised 21 May 2017 (this version, v2) | v2: 24 pages, minor corrections, exposition improved, especially in Section 6; added references | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1603.03929 | We supply a detailed proof of the result by P.S. Green and T. H$\ddot{\text{u}}$bsch that all complete intersection Calabi--Yau 3-folds in product of projective spaces are connected through projective conifold transitions (known as the standard web). We also introduce a subclass of small transitions which we call primi... | math-32-part-1.zip/1603.03929.pdf |
1301.6889 | Abundance theorem for semi log canonical surfaces in positive characteristic | [
"Hiromu Tanaka"
] | 29 Jan 2013 (<a href="https://arxiv.org/abs/1301.6889v1">v1</a>), last revised 19 Oct 2015 (this version, v3) | 33 pages. v2: I added Section 3, changed the definition of slc surfaces, and adopted the one of Kollar. v3: minor changes | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1301.6889 | We prove the abundance theorem for semi log canonical surfaces in positive characteristic. | math-31-part-2.zip/1301.6889.pdf |
2303.13201 | Positivity and base loci for vector bundles revisited | [
"Mihai Fulger",
"Nabanita Ray"
] | 23 Mar 2023 | 16 pages, comments welcomed | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2303.13201 | We give equivalent descriptions for the augmented and diminished base loci of vector bundles in characteristic zero. We show that these base loci behave well under pullback, tensor product, and direct sum. Pathological behavior is observed on some nonsplit exact sequences. | math-33-part-2.zip/2303.13201.pdf |
1403.0984 | A marvellous embedding of the Lagrangian Grassmannian | [
"Kevin Purbhoo"
] | 5 Mar 2014 | 26 pages, 7 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.1403.0984 | We give a embedding of the Lagrangian Grassmannian LG(n) inside an ordinary Grassmannian that is well-behaved with respect to the Wronski map. As a consequence, we obtain an analogue of the Mukhin-Tarasov-Varchenko theorem for LG(n). The restriction of the Wronski map to LG(n) has degree equal to the number of shifted ... | math-31-part-2.zip/1403.0984.pdf |
1802.05398 | Pre-Calabi-Yau structures and moduli of representations | [
"Wai-Kit Yeung"
] | 15 Feb 2018 (<a href="https://arxiv.org/abs/1802.05398v1">v1</a>), last revised 19 Feb 2022 (this version, v4) | 32 pages, 3 figures. Comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); K-Theory and Homology (math.KT); Representation Theory (math.RT); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.1802.05398 | We establish a system of formal noncommutative calculus for differential forms and polyvector fields, which forms the foundations for the study of pre-Calabi-Yau categories. Using an explicit trace map, we show that any $n$-Calabi-Yau structure on a non-positively graded dg algebra $A$ induces a $(2-n)$-shifted symplec... | math-32-part-2.zip/1802.05398.pdf |
1008.2480 | Any component of moduli of polarized hyperkaehler manifolds is dense in its deformation space | [
"Sasha Anan'in",
"Misha Verbitsky"
] | 14 Aug 2010 (<a href="https://arxiv.org/abs/1008.2480v1">v1</a>), last revised 8 Oct 2012 (this version, v5) | 17 pages, 4 figures, v. 5.0, the introduction is cleaned up, a reference to [KV] added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1008.2480 | Let M be a compact hyperkaehler manifold, and W the coarse moduli of complex deformations of M. Every positive integer class v in $H^2(M)$ defines a divisor $D_v$ in W consisting of all algebraic manifolds polarized by v. We prove that every connected component of this divisor is dense in W. | math-31-part-1.zip/1008.2480.pdf |
1506.04900 | Surfaces of globally $F$-regular type are of Fano type | [
"Shinnosuke Okawa"
] | 16 Jun 2015 | 10 pages. To appear in Tohoku Mathematical Journal | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1506.04900 | We prove that a projective surface of globally $F$-regular type defined over a field of characteristic zero is of Fano type. | math-32-part-1.zip/1506.04900.pdf |
2005.03689 | Moduli of linear slices of high degree hypersurfaces | [
"Anand Patel",
"Eric Riedl",
"Dennis Tseng"
] | 7 May 2020 (<a href="https://arxiv.org/abs/2005.03689v1">v1</a>), last revised 19 Jan 2022 (this version, v2) | Fixed a typo in Proposition 3.1 (the connected fibers hypothesis was left out of the previous version) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2005.03689 | We study the variation of linear sections of hypersurfaces in $\mathbb{P}^n$. We completely classify all plane curves, necessarily singular, whose line sections do not vary maximally in moduli. In higher dimensions, we prove that the family of hyperplane sections of any smooth degree $d$ hypersurface in $\mathbb{P}^n$ ... | math-32-part-2.zip/2005.03689.pdf |
1610.05720 | Motivic random variables and representation stability II: Hypersurface sections | [
"Sean Howe"
] | 18 Oct 2016 (<a href="https://arxiv.org/abs/1610.05720v1">v1</a>), last revised 24 Mar 2020 (this version, v2) | 37 pages, close to final journal version. Major update from v1: the main conjecture of v1 is the main theorem of v2 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Geometric Topology (math.GT); Number Theory (math.NT); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1610.05720 | We prove geometric and cohomological stabilization results for the universal smooth degree $d$ hypersurface section of a fixed smooth projective variety as $d$ goes to infinity. We show that relative configuration spaces of the universal smooth hypersurface section stabilize in the completed Grothendieck ring of variet... | math-32-part-1.zip/1610.05720.pdf |
1701.08372 | Stable rationality of del Pezzo fibrations of low degree over projective spaces | [
"Igor Krylov",
"Takuzo Okada"
] | 29 Jan 2017 | 30 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1701.08372 | The main aim of this article is to show that a very general 3-dimensional del Pezzo fibration of degree 1,2,3 is not stably rational except for a del Pezzo fibration of degree 3 belonging to explicitly described 2 families. Higher dimensional generalizations are also discussed and we prove that a very general del Pezzo... | math-32-part-1.zip/1701.08372.pdf |
math/0204002 | Bertini theorems over finite fields | [
"Bjorn Poonen"
] | 29 Mar 2002 | 22 pages, Latex 2e | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.math/0204002 | Let X be a smooth quasiprojective subscheme of P^n of dimension m >= 0 over F_q. Then there exist homogeneous polynomials f over F_q for which the intersection of X and the hypersurface f=0 is smooth. In fact, the set of such f has a positive density, equal to zeta_X(m+1)^{-1}, where zeta_X(s)=Z_X(q^{-s}) is the zet... | math-34-part-1.zip/math_0204002.pdf |
1808.10070 | On subgroups of an automorphism group of an irreducible symplectic manifold | [
"Daisuke Matsushita"
] | 30 Aug 2018 (<a href="https://arxiv.org/abs/1808.10070v1">v1</a>), last revised 28 Dec 2018 (this version, v2) | Correct typo and give a new proof of Lemma 5.1 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1808.10070 | Let X be an irreducible symplectic manifold and L a nef line bundle on X which is isotropic with respect to the Beauville-Bogomolov quadratic form. It is known that a subgroup Aut(X,L) of an automorphism group of X which fix L is almost abelian. We give a formula of the rank of Aut(X,L) in terms of MBM divisors. We als... | math-32-part-2.zip/1808.10070.pdf |
1112.1080 | Remarks on motives of abelian type | [
"Charles Vial"
] | 5 Dec 2011 (<a href="https://arxiv.org/abs/1112.1080v1">v1</a>), last revised 27 Jul 2015 (this version, v3) | 21 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1112.1080 | A motive over a field $k$ is of abelian type if it belongs to the thick and rigid subcategory of Chow motives spanned by the motives of abelian varieties over $k$. This paper contains three sections of independent interest. First, we show that a motive which becomes of abelian type after a base field extension of algeb... | math-31-part-2.zip/1112.1080.pdf |
2203.10617 | Explicit formulae for rank zero DT invariants and the OSV conjecture | [
"Soheyla Feyzbakhsh"
] | 20 Mar 2022 | 34 pages, 4 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th) | https://doi.org/10.48550/arXiv.2203.10617 | Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as the quintic 3-fold. By two different wall-crossing arguments we prove two different explicit formulae relating rank 0 Donaldson-Thomas invariants (counting torsion sheaves on $X$ supported on ample divisors) in terms o... | math-33-part-1.zip/2203.10617.pdf |
math/0511656 | Rationality and Poincare families for vector bundles with extra structure on a curve | [
"Norbert Hoffmann"
] | 27 Nov 2005 | 19 pages AMSLaTeX | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0511656 | Iterated Grassmannian bundles over moduli stacks of vector bundles on a curve are shown to be birational to an affine space times a moduli stack of degree 0 vector bundles, following the method of King and Schofield. Applications include the birational type of some Brill-Noether loci, of moduli schemes for vector bundl... | math-34-part-1.zip/math_0511656.pdf |
1711.04535 | On an open problem of characterizing the birationality of 4K | [
"Meng Chen",
"Yong Hu"
] | 13 Nov 2017 (<a href="https://arxiv.org/abs/1711.04535v1">v1</a>), last revised 18 Jun 2018 (this version, v3) | 11 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1711.04535 | We answer an open problem raised by Chen and Zhang in 2008 and prove that, for any minimal projective 3-fold $X$ of general type with the geometric genus $\geq 5$, $X$ is birationally fibred by a pencil of $(1,2)$-surfaces (i.e. $c_1^2=1$, $p_g=2$) if and only if the $4$-canonical map $\varphi_{4,X}$ is non-birational.... | math-32-part-1.zip/1711.04535.pdf |
1102.4184 | Non-normal abelian covers | [
"Valery Alexeev",
"Rita Pardini"
] | 21 Feb 2011 (<a href="https://arxiv.org/abs/1102.4184v1">v1</a>), last revised 10 Oct 2011 (this version, v3) | To appear in Compositio Mathematica. This version is slightly different | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1102.4184 | An abelian cover is a finite morphism $X\to Y$ of varieties which is the quotient map for a generically faithful action of a finite abelian group $G$. Abelian covers with $Y$ smooth and $X$ normal were studied in \cite{Pardini_AbelianCovers}. <br>Here we study the non-normal case, assuming that $X$ and $Y$ are $S_2$ va... | math-31-part-1.zip/1102.4184.pdf |
2202.09397 | The theta invariants and the volume function on arithmetic varieties | [
"Mounir Hajli"
] | 18 Feb 2022 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2202.09397 | We introduce a new arithmetic invariant for hermitian line bundles on an arithmetic variety. We use this invariant to measure the variation of the volume function with respect to the metric. The main result of this paper is a generalized Hodge index theorem on arithmetic toric varieties. | math-33-part-1.zip/2202.09397.pdf | |
1505.02249 | Complete intersections: Moduli, Torelli, and good reduction | [
"Ariyan Javanpeykar",
"Daniel Loughran"
] | 9 May 2015 (<a href="https://arxiv.org/abs/1505.02249v1">v1</a>), last revised 1 Aug 2016 (this version, v2) | 37 pages. Typo's fixed. Expanded Section 2.5 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1505.02249 | We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings. For example, we prove an analogue of the Shafarevich conjecture for cubic and... | math-32-part-1.zip/1505.02249.pdf |
0809.2749 | Ruan's conjecture and integral structures in quantum cohomology | [
"Hiroshi Iritani"
] | 16 Sep 2008 | 38 pages; Submitted to the proceedings of the conference "New developments in Algebraic Geometry, Integrable Systems and Mirror symmetry" held at RIMS, January, 2008 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.0809.2749 | This is an expository article on the recent studies of Ruan's crepant resolution/flop conjecture and its possible relations to the K-theory integral structure in quantum cohomology. | math-31-part-1.zip/0809.2749.pdf |
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