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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1809.06566 | Lattices for Landau-Ginzburg orbifolds | [
"Wolfgang Ebeling",
"Atsushi Takahashi"
] | 18 Sep 2018 | 23 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1809.06566 | We consider a pair consisting of an invertible polynomial and a finite abelian group of its symmetries. Berglund, Hübsch, and Henningson proposed a duality between such pairs giving rise to mirror symmetry. We define an orbifoldized signature for such a pair using the orbifoldized elliptic genus. In the case of three v... | math-32-part-2.zip/1809.06566.pdf |
1605.03846 | Non-arithmetic lattices and the Klein quartic | [
"Martin Deraux"
] | 12 May 2016 (<a href="https://arxiv.org/abs/1605.03846v1">v1</a>), last revised 21 Jan 2017 (this version, v4) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Differential Geometry (math.DG); Geometric Topology (math.GT) | https://doi.org/10.48550/arXiv.1605.03846 | We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship between the corresponding orbifold fundamental groups and the automorphism group of the Klein quartic, and also with groups constructed by Bar... | math-32-part-1.zip/1605.03846.pdf | |
math/0607012 | The spaces of Laurent polynomials, $\mathbb{P}^1$-orbifolds, and integrable hierarchies | [
"Todor E. Milanov",
"Hsian-Hua Tseng"
] | 1 Jul 2006 (<a href="https://arxiv.org/abs/math/0607012v1">v1</a>), last revised 4 Sep 2007 (this version, v3) | v2: Typos and mistakes fixed, to appear in Journal fuer die reine und angewandte Mathematik (Crelle's Journal). v3: Mistakes fixed and references updated | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.math/0607012 | Let $M_{k,m}$ be the space of Laurent polynomials in one variable $x^k + t_1 x^{k-1}+... t_{k+m}x^{-m},$ where $k,m\geq 1$ are fixed integers and $t_{k+m}\neq 0$. According to B. Dubrovin \cite{D}, $M_{k,m}$ can be equipped with a semi-simple Frobenius structure. In this paper we prove that the corresponding descendant... | math-34-part-1.zip/math_0607012.pdf |
1906.00118 | A Universal HKR Theorem | [
"Tasos Moulinos",
"Marco Robalo",
"Bertrand Toën"
] | 31 May 2019 (<a href="https://arxiv.org/abs/1906.00118v1">v1</a>), last revised 11 Mar 2021 (this version, v3) | 105 pages. New section comparing our filtration with the one of Antieau and Bhatt-Morrow-Scholze. To appear in Geometry and Topology | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); K-Theory and Homology (math.KT); Number Theory (math.NT); Quantum Algebra (math.QA) | https://doi.org/10.48550/arXiv.1906.00118 | In this work we study the failure of the HKR theorem over rings of positive and mixed characteristic. For this we construct a filtered circle interpolating between the usual topological circle and a formal version of it. By mapping to schemes we produce this way an interpolation, realized in practice by the existence o... | math-32-part-2.zip/1906.00118.pdf |
1711.04108 | Holomorphic aspects of moduli of representations of quivers | [
"Pradeep Das",
"S. Manikandan",
"N. Raghavendra"
] | 11 Nov 2017 | 40 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1711.04108 | This article describes some complex-analytic aspects of the moduli space of the finite-dimensional complex representations of a finite quiver, which are stable with respect to a fixed rational weight. We construct a natural structure of a complex manifold on this moduli space, and a Kähler metric on the complex manifol... | math-32-part-1.zip/1711.04108.pdf |
0807.4539 | Resultants and Contour Integrals | [
"A.Morozov",
"Sh.Shakirov"
] | 28 Jul 2008 | 9 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.0807.4539 | Resultants are important special functions used in description of non-linear phenomena. Resultant $R_{r_1, ..., r_n}$ defines a condition of solvability for a system of $n$ homogeneous polynomials of degrees $r_1, ..., r_n$ in $n$ variables, just in the same way as determinant does for a system of linear equations. Unf... | math-31-part-1.zip/0807.4539.pdf |
0804.3651 | Monodromy Filtrations and the Topology of Tropical Varieties | [
"David Helm",
"Eric Katz"
] | 23 Apr 2008 (<a href="https://arxiv.org/abs/0804.3651v1">v1</a>), last revised 16 Jan 2011 (this version, v5) | 22 pages. Canadian Journal of Mathematics, to appear | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0804.3651 | We find restrictions on the topology of tropical varieties that arise from a certain natural class of varieties. We develop a theory of tropical degenerations that is a nonconstant coefficient analogue of Tevelev's theory of tropical compactifications, and use it to construct normal crossings degenerations of a sub... | math-31-part-1.zip/0804.3651.pdf |
1304.3883 | On caustics by reflection of algebraic surfaces | [
"Alfrederic Josse",
"Francoise Pene"
] | 14 Apr 2013 (<a href="https://arxiv.org/abs/1304.3883v1">v1</a>), last revised 26 Jun 2014 (this version, v2) | 31 pages, 9 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1304.3883 | Given a point S (the light position) in P^3 and an algebraic surface Z (the mirror) of P^3, the caustic by reflection of Z from S is the Zariski closure of the envelope of the reflected lines got by reflection of the incident lines (Sm) on Z at m in Z. We use the ramification method to identify the caustic by reflectio... | math-31-part-2.zip/1304.3883.pdf |
2401.00489 | Hodge Theory of Abelian Covers | [
"Eva Elduque",
"Moisés Herradón Cueto"
] | 31 Dec 2023 (<a href="https://arxiv.org/abs/2401.00489v1">v1</a>), last revised 17 Jul 2024 (this version, v2) | 72 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.2401.00489 | Motivated by classical Alexander invariants of affine hypersurface complements, we endow certain finite dimensional quotients of the homology of abelian covers of complex algebraic varieties with a canonical and functorial mixed Hodge structure (MHS). More precisely, we focus on covers which arise algebraically in the ... | math-33-part-2.zip/2401.00489.pdf |
1602.02996 | Stability of test ideals of divisors with small multiplicity | [
"Kenta Sato"
] | 9 Feb 2016 (<a href="https://arxiv.org/abs/1602.02996v1">v1</a>), last revised 20 Aug 2017 (this version, v2) | 21pages; v2; Proposition-Definition 2.19 of our previous version was not correct, see Remark 2.20 for details, references added, several typos fixed, to appear in Mathematische Zeitschrift | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1602.02996 | Let $(X, \Delta)$ be a log pair in characteristic $p>0$ and $P$ be a (not necessarily closed) point of $X$. We show that there exists a constant $\delta>0$ such that $\tau(X, \Delta)_P= \tau(X, \Delta + D)_P$ for each effective $\mathbb{Q}$-Cartier divisor $D$ with $\mathrm{mult}_P(D) <\delta$. As its applicat... | math-32-part-1.zip/1602.02996.pdf |
2502.06365 | Algebraic hyperbolicity of surfaces in Fano threefolds with Picard number one | [
"Haesong Seo"
] | 10 Feb 2025 | 25 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2502.06365 | In this paper, we study the algebraic hyperbolicity of very general surfaces in general Fano threefolds with Picard number one. We completely classify the algebraically hyperbolicity of those surfaces, except for surfaces in weighted hypersurfaces. | math-33-part-2.zip/2502.06365.pdf |
1708.06076 | The equations defining affine Grassmannians in type A and a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman | [
"Dinakar Muthiah",
"Alex Weekes",
"Oded Yacobi"
] | 21 Aug 2017 (<a href="https://arxiv.org/abs/1708.06076v1">v1</a>), last revised 14 Jun 2018 (this version, v2) | 33 pages, comments welcome; (v2) corrected typos, revised Sections 1.1, 3.1.5, 4.3 and argument in proof of Theorem 5.10, results unchanged | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1708.06076 | The affine Grassmannian of $SL_n$ admits an embedding into the Sato Grassmannian, which further admits a Plücker embedding into the projectivization of Fermion Fock space. Kreiman, Lakshmibai, Magyar, and Weyman describe the linear part of the ideal defining this embedding in terms of certain elements of the dual of Fo... | math-32-part-1.zip/1708.06076.pdf |
1908.03563 | Additive actions on complete toric surfaces | [
"Sergey Dzhunusov"
] | 7 Aug 2019 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1908.03563 | By an additive action on an algebraic variety $X$ we mean a regular effective action $\mathbb{G}_a^n\times X\to X$ with an open orbit of the commutative unipotent group $\mathbb{G}_a^n$. In this paper, we give a classification of additive actions on complete toric surfaces. | math-32-part-2.zip/1908.03563.pdf | |
1503.04243 | Convergent isocrystals on simply connected varieties | [
"Hélène Esnault",
"Atsushi Shiho"
] | 13 Mar 2015 (<a href="https://arxiv.org/abs/1503.04243v1">v1</a>), last revised 12 Apr 2016 (this version, v2) | 36 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1503.04243 | It is conjectured by de Jong that, if $X$ is a connected smooth projective variety over an algebraically closed field $k$ of characteristic $p>0$ with trivial étale fundamental group, any isocrystal on on $X/W$ is trivial. We prove this conjecture under two additional assumptions. Version 2: the main change is an ad... | math-32-part-1.zip/1503.04243.pdf |
1009.4372 | Stability conditions via spherical objects | [
"Daniel Huybrechts"
] | 22 Sep 2010 | 19 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1009.4372 | An object in the bounded derived category D^b(Coh(X)) of coherent sheaves on a complex projective K3 surface X is spherical if it is rigid and simple. Although spherical objects form only a discrete set in the moduli stack of complexes, they determine much of the structure of X and D^b(Coh(X)). Here we show that a stab... | math-31-part-1.zip/1009.4372.pdf |
math/9809140 | The Abel-Jacobi map of a moduli component of vector bundles on the cubic threefold | [
"D. Markushevich",
"A. S. Tikhomirov"
] | 24 Sep 1998 (<a href="https://arxiv.org/abs/math/9809140v1">v1</a>), last revised 13 Aug 1999 (this version, v3) | Final version, as accepted in JAG | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/9809140 | The Abel-Jacobi map of the family of elliptic quintics lying on a general cubic threefold is studied. It is proved that it factors through a moduli component of stable rank 2 vector bundles on the cubic threefold with Chern numbers c_1=0, c_2=2, whose general point represents a vector bundle obtained by Serre's con... | math-34-part-2.zip/math_9809140.pdf |
1411.2325 | Smoothing of Limit Linear Series of Rank One on Saturated Metrized Complexes of Algebraic Curves | [
"Ye Luo",
"Madhusudan Manjunath"
] | 10 Nov 2014 (<a href="https://arxiv.org/abs/1411.2325v1">v1</a>), last revised 29 Jun 2017 (this version, v4) | 44 pages (Appendix included) 11 Figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1411.2325 | We investigate the smoothing problem of limit linear series of rank one on an enrichment of the notions of nodal curves and metrized complexes called saturated metrized complexes. We give a finitely verifiable full criterion for smoothability of a limit linear series of rank one on saturared metrized complexes, charact... | math-31-part-2.zip/1411.2325.pdf |
2210.04587 | Toric sheaves, stability and fibrations | [
"Achim Napame",
"Carl Tipler"
] | 10 Oct 2022 (<a href="https://arxiv.org/abs/2210.04587v1">v1</a>), last revised 27 Jul 2023 (this version, v2) | Final version. For the study of stability, we now assume that X and X' are Q-factorial projective toric varieties. To appear in ``Journal of Pure and Applied Algebra'' | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2210.04587 | For an equivariant reflexive sheaf over a polarised toric variety, we study slope stability of its reflexive pullback along a toric fibration. Examples of such fibrations include equivariant blow-ups and toric locally trivial fibrations. We show that stability (resp. unstability) is preserved under such pullbacks for s... | math-33-part-1.zip/2210.04587.pdf |
2301.01196 | Logarithmic Quasimaps | [
"Qaasim Shafi"
] | 3 Jan 2023 (<a href="https://arxiv.org/abs/2301.01196v1">v1</a>), last revised 12 Jan 2024 (this version, v2) | Final version to appear in Advances in Mathematics | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2301.01196 | We construct a proper moduli space which is a Deligne-Mumford stack parametrising quasimaps relative to a simple normal crossings divisor in any genus using logarithmic geometry. We show this moduli space admits a virtual fundamental class of the expected dimension leading to numerical invariants which agree with the t... | math-33-part-1.zip/2301.01196.pdf |
0706.2501 | Matching polytopes, toric geometry, and the non-negative part of the Grassmannian | [
"Alexander Postnikov",
"David Speyer",
"Lauren Williams"
] | 17 Jun 2007 (<a href="https://arxiv.org/abs/0706.2501v1">v1</a>), last revised 14 Oct 2008 (this version, v3) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.0706.2501 | In this paper we use toric geometry to investigate the topology of the totally non-negative part of the Grassmannian (Gr_{kn})_{\geq 0}. This is a cell complex whose cells Delta_G can be parameterized in terms of the combinatorics of plane-bipartite graphs G. To each cell Delta_G we associate a certain polytope P(G). T... | math-30-part-2.zip/0706.2501.pdf | |
2303.06940 | A geometrization of Stanley--Reisner theory | [
"Fernando Sancho de Salas",
"Alejandro Torres Sancho"
] | 13 Mar 2023 (<a href="https://arxiv.org/abs/2303.06940v1">v1</a>), last revised 30 Jun 2023 (this version, v4) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.2303.06940 | We give a geometric interpretation of the Stanley--Reisner correspondence, extend it to schemes, and interpret it in terms of the field of one element. | math-33-part-2.zip/2303.06940.pdf | |
1612.08101 | Shifted cotangent stacks are shifted symplectic | [
"Damien Calaque"
] | 23 Dec 2016 (<a href="https://arxiv.org/abs/1612.08101v1">v1</a>), last revised 8 Mar 2017 (this version, v2) | 16 pages. Minor corrections. To appear in Annales de la Faculté des Sciences de Toulouse | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.1612.08101 | We prove that shifted cotangent stacks carry a canonical shifted symplectic structure. We also prove that shifted conormal stacks carry a canonical Lagrangian structure. These results were believed to be true but no written proof was available in the Artin case. | math-32-part-1.zip/1612.08101.pdf |
1901.06689 | Birationally superrigid Fano 3-folds of codimension 4 | [
"Takuzo Okada"
] | 20 Jan 2019 | 18 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1901.06689 | We determine birational superrigidity for a quasi-smooth prime Fano 3-fold of codimension 4 with no projection centers. In particular we prove birational superrigidity for Fano 3-folds of codimension 4 with no projection centers which are recently constructed by Coughlan and Ducat. We also pose some questions and a con... | math-32-part-2.zip/1901.06689.pdf |
1505.05729 | Eigenconfigurations of Tensors | [
"Hirotachi Abo",
"Anna Seigal",
"Bernd Sturmfels"
] | 21 May 2015 (<a href="https://arxiv.org/abs/1505.05729v1">v1</a>), last revised 19 Dec 2015 (this version, v2) | 25 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Dynamical Systems (math.DS); Optimization and Control (math.OC); Spectral Theory (math.SP) | https://doi.org/10.48550/arXiv.1505.05729 | Square matrices represent linear self-maps of vector spaces, and their eigenpoints are the fixed points of the induced map on projective space. Likewise, polynomial self-maps of a projective space are represented by tensors. We study the configuration of fixed points of a tensor or symmetric tensor. | math-32-part-1.zip/1505.05729.pdf |
math/0309444 | Hitchin's connection and differential operators with values in the determinant bundle | [
"Xiaotao Sun",
"I-Hsun Tsai"
] | 27 Sep 2003 | 32 pages, Latex | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0309444 | Let $C/M$ be a local universal family of smooth curves and $S/M$ be the family of moduli spaces of stable bundles with a fixed determinant on curves. In this paper, we find locally free sheaves $\Cal G_E$, $S(\Cal G_E)$ on $X=C\times_M S$ such that their first direct images are isomorphic to sheaves $\Cal D^{\le 1}_{S/... | math-34-part-1.zip/math_0309444.pdf |
0712.0723 | Dominance of a Rational Map to the Coble Quartic | [
"Sukmoon Huh"
] | 5 Dec 2007 (<a href="https://arxiv.org/abs/0712.0723v1">v1</a>), last revised 5 Nov 2008 (this version, v5) | 11 pages, Remark 3.5 added, the title changed | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0712.0723 | We show the dominance of the restriction map from a moduli space of stable sheaves on the projective plane to the Coble quartic. With the dominance and the interpretation of a stable sheaf on the plane in terms of the hyperplane arrangements, we expect to investigate the geometry of the Coble quartic. | math-31-part-1.zip/0712.0723.pdf |
1806.09794 | Twistor triangles in the period domain of complex tori | [
"Nikolay Buskin"
] | 26 Jun 2018 (<a href="https://arxiv.org/abs/1806.09794v1">v1</a>), last revised 5 Jan 2019 (this version, v3) | 28 pages, 3 figures, an erroneous statement in the third theorem about the diffeomorphism types of the connected components of the fiber of the multiplication map has been corrected, the proof has been rewritten. Some general editing of the text | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV); Differential Geometry (math.DG); Rings and Algebras (math.RA); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1806.09794 | We study the geometry of the (generalized) twistor triangles $\triangle J_1J_2J_3$ in the period domain of compact complex tori of complex dimension $2n$ by the means of the representation theory of the algebras (of real dimension 8) generated by the complex structures $J_1,J_2,J_3$. Considering the period domain as th... | math-32-part-2.zip/1806.09794.pdf |
1411.7849 | Cocharacter-closure and the rational Hilbert-Mumford Theorem | [
"Michael Bate",
"Sebastian Herpel",
"Benjamin Martin",
"Gerhard Roehrle"
] | 28 Nov 2014 (<a href="https://arxiv.org/abs/1411.7849v1">v1</a>), last revised 3 Oct 2016 (this version, v5) | 33 pages, v. 2 reference added, slight changes, v. 3 minor changes, v. 4 added new Thm 1.6 characterizing k-anisotropic reductive groups in terms of cocharacter-closure; v. 5 final version, further small changes; to appear in Math. Z | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Group Theory (math.GR) | https://doi.org/10.48550/arXiv.1411.7849 | For a field k, let G be a reductive k-group and V an affine k-variety on which G acts. Using the notion of cocharacter-closed G(k)-orbits in V, we prove a rational version of the celebrated Hilbert-Mumford Theorem from geometric invariant theory. We initiate a study of applications stemming from this rationality tool. ... | math-31-part-2.zip/1411.7849.pdf |
2402.10209 | Good models of Hilbert schemes of points over semistable degenerations | [
"Calla Tschanz"
] | 15 Feb 2024 | 40 pages, 6 Figures. Comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2402.10209 | In this paper, we explore different possible choices of expanded degenerations and define appropriate stability conditions in order to construct good degenerations of Hilbert schemes of points over semistable degenerations of surfaces, given as proper Deligne-Mumford stacks. These stacks provide explicit examples of co... | math-33-part-2.zip/2402.10209.pdf |
math/0509224 | Lagrangian fibrations on Hilbert schemes of points on K3 surfaces | [
"Justin Sawon"
] | 9 Sep 2005 (<a href="https://arxiv.org/abs/math/0509224v1">v1</a>), last revised 7 Oct 2005 (this version, v3) | 21 pages, original (stronger) version of Theorem 2 proved | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0509224 | Let $\mathrm{Hilb}^gS$ be the Hilbert scheme of $g$ points on a K3 surface $S$. Suppose that $\mathrm{Pic}S\cong\Z C$ where $C$ is a smooth curve with $C^2=2(g-1)n^2$. We prove that $\mathrm{Hilb}^gS$ is a Lagrangian fibration. | math-34-part-1.zip/math_0509224.pdf |
2406.05550 | Descent for Algebraic Schemes | [
"James S Milne"
] | 8 Jun 2024 | 27 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2406.05550 | This is an elementary exposition of the basic descent theorems for algebraic schemes over fields (Grothendieck, Weil, ...). | math-33-part-2.zip/2406.05550.pdf |
1501.00859 | Absolutely split locally free sheaves on proper $k$-schemes and Brauer--Severi varieties | [
"Saša Novaković"
] | 5 Jan 2015 (<a href="https://arxiv.org/abs/1501.00859v1">v1</a>), last revised 5 Apr 2018 (this version, v2) | 17 pages, revised version with corrected and improved result, comments are welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1501.00859 | We classify absolutely split vector bundles on proper $k$-schemes. More precise, we prove that the closed points of the Picard scheme are in one-to-one correspondence with indecomposable absolutely split vector bundles. Furthermore, we apply the obtained results to study the geometry of (generalized) Brauer--Severi var... | math-31-part-2.zip/1501.00859.pdf |
1810.07777 | On the derived category of $\mathrm{IGr}(3,8)$ | [
"Lyalya Guseva"
] | 17 Oct 2018 (<a href="https://arxiv.org/abs/1810.07777v1">v1</a>), last revised 10 Dec 2018 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1810.07777 | We construct a full exceptional collection of vector bundles in the bounded derived category of coherent sheaves on the Grassmannian $\mathrm{IGr}(3,8)$ of isotropic 3-dimensional subspaces in an 8-dimensional symplectic vector space. | math-32-part-2.zip/1810.07777.pdf | |
1211.2621 | Remarks On the Topology of the Fano surface | [
"Alberto Collino"
] | 12 Nov 2012 (<a href="https://arxiv.org/abs/1211.2621v1">v1</a>), last revised 19 Apr 2014 (this version, v2) | References added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1211.2621 | We analize the semistable degeneration of the Fano surface F when the cubic threefold becomes the Segre primal. This gives an explicit topological decomposition for F. The decomposition is used to decide that the Fano surface is not an an Eilenberg Mac-Lane K(\pi,1) space, this was the question that prompted us to look... | math-31-part-2.zip/1211.2621.pdf |
0810.0924 | The Neron model over the Igusa curves | [
"Christian Liedtke",
"Stefan Schroeer"
] | 6 Oct 2008 (<a href="https://arxiv.org/abs/0810.0924v1">v1</a>), last revised 3 May 2010 (this version, v2) | 44 pages, minor changes | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.0810.0924 | We analyze the geometry of rational p-division points in degenerating families of elliptic curves in characteristic p. We classify the possible Kodaira symbols and determine for the Igusa moduli problem the reduction type of the universal curve. Special attention is paid to characteristic 2 and 3 where wild ramificatio... | math-31-part-1.zip/0810.0924.pdf |
1110.5683 | Line Bundles and Curves on a del Pezzo Order | [
"Boris Lerner"
] | 25 Oct 2011 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Rings and Algebras (math.RA) | https://doi.org/10.48550/arXiv.1110.5683 | Orders on surfaces provide a rich source of examples of noncommutative surfaces. Other than some existence results, very little is known about the various moduli spaces that can be associated to them. Even fewer examples have been explicitly computed. In this paper we compute the Picard and Hilbert schemes of an order ... | math-31-part-2.zip/1110.5683.pdf | |
1102.1312 | Mixed Tate motives over $\Z$ | [
"Francis Brown"
] | 7 Feb 2011 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1102.1312 | We prove that the category of mixed Tate motives over $\Z$ is spanned by the motivic fundamental group of $\Pro^1$ minus three points. We prove a conjecture by M. Hoffman which states that every multiple zeta value is a $\Q$-linear combination of $\zeta(n_1,..., n_r)$ where $n_i\in \{2,3\}$. | math-31-part-1.zip/1102.1312.pdf | |
0712.3374 | Fundamental groups of moduli stacks of smooth Weierstrass fibrations | [
"Michael Lönne"
] | 20 Dec 2007 | 38 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0712.3374 | We give finite presentations for the fundamental group of moduli stacks of smooth Weierstrass curves over complex projective space P^n which extend the classical result for elliptic curves to positive dimensional base. We thus get natural generalisations of SL_2(Z) and pave the way to understanding the fundamental grou... | math-31-part-1.zip/0712.3374.pdf |
math/9912229 | Toric Prevarieties and Subtorus Actions | [
"A. A'Campo-Neuen",
"J. Hausen"
] | 30 Dec 1999 | 24 pages, 5 figures, LaTeX2e+pstex | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/9912229 | Dropping separatedness in the definition of a toric variety, one obtains the more general notion of a toric prevariety. Toric prevarieties occur as ambient spaces in algebraic geometry and moreover they appear naturally as intermediate steps in quotient constructions. We first provide a complete description of the cate... | math-34-part-2.zip/math_9912229.pdf |
1205.3602 | Stability conditions and birational geometry of projective surfaces | [
"Yukinobu Toda"
] | 16 May 2012 (<a href="https://arxiv.org/abs/1205.3602v1">v1</a>), last revised 12 Nov 2013 (this version, v2) | 39 pages, to appear in Compositio Mathematica | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1205.3602 | We show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves. | math-31-part-2.zip/1205.3602.pdf |
1305.4687 | From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives | [
"Marcello Bernardara",
"Goncalo Tabuada"
] | 21 May 2013 (<a href="https://arxiv.org/abs/1305.4687v1">v1</a>), last revised 27 May 2014 (this version, v2) | Revised version. In particular, a new class of examples was added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT); K-Theory and Homology (math.KT) | https://doi.org/10.48550/arXiv.1305.4687 | Let X and Y be complex smooth projective varieties, and D^b(X) and D^b(Y) the associated bounded derived categories of coherent sheaves. Assume the existence of a triangulated category T which is admissible both in D^b(X) as in D^b(Y). Making use of the recent theory of Jacobians of noncommutative motives, we construct... | math-31-part-2.zip/1305.4687.pdf |
2112.03117 | Strictly nef divisors on singular threefolds | [
"Juanyong Wang",
"Guolei Zhong"
] | 6 Dec 2021 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2112.03117 | Let $X$ be a normal projective variety with only klt singularities, and $L_X$ a strictly nef $\mathbb{Q}$-divisor on $X$. In this paper, we study the singular version of Serrano's conjecture, i.e., the ampleness of $K_X+t L_X$ for sufficiently large $t\gg 1$. We show that, if $X$ is assumed to be a $\mathbb{Q}$-fac... | math-33-part-1.zip/2112.03117.pdf | |
1511.01262 | Artin approximation compatible with a change of variables | [
"Goulwen Fichou",
"Ronan Quarez",
"Masahiro Shiota"
] | 4 Nov 2015 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1511.01262 | We propose a version of the classical Artin approximation which allows to perturb the variables of the approximated solution. Namely, it is possible to approximate a formal solution of a Nash equation by a Nash solution in a compatible way with a given Nash change of variables. This results is closely related to the so... | math-32-part-1.zip/1511.01262.pdf | |
2002.09698 | Monodromy of projections of hypersurfaces | [
"Maria Gioia Cifani",
"Alice Cuzzucoli",
"Riccardo Moschetti"
] | 22 Feb 2020 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2002.09698 | Let $X$ be an irreducible, reduced complex projective hypersurface of degree $d$. A point $P$ not contained in $X$ is called uniform if the monodromy group of the projection of $X$ from $P$ is isomorphic to the symmetric group $S_d$. We prove that the locus of non--uniform points is finite when $X$ is smooth or a gener... | math-32-part-2.zip/2002.09698.pdf | |
2112.12736 | On the Hodge-BGW correspondence | [
"Di Yang",
"Qingsheng Zhang"
] | 23 Dec 2021 (<a href="https://arxiv.org/abs/2112.12736v1">v1</a>), last revised 16 Jan 2022 (this version, v2) | It was added a new application in the Appendix; added references; corrected typos; 25 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI) | https://doi.org/10.48550/arXiv.2112.12736 | We establish an explicit relationship between the partition function of certain special cubic Hodge integrals and the generalized Brezin--Gross--Witten (BGW) partition function, which we refer to as the Hodge-BGW correspondence. As an application, we obtain an ELSV-like formula for generalized BGW correlators. | math-33-part-1.zip/2112.12736.pdf |
math/9909074 | Abelian fibrations and rational points on symmetric products | [
"Brendan Hassett",
"Yuri Tschinkel"
] | 14 Sep 1999 | 17 pages, LaTeX | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.math/9909074 | Given a variety over a number field, are its rational points potentially dense, i.e., does there exist a finite extension over which rational points are Zariski dense? We study the question of potential density for symmetric products of surfaces. Contrary to the situation for curves, rational points are not necessarily... | math-34-part-2.zip/math_9909074.pdf |
2010.11275 | Determinant of $\mathbb F_p$-hypergeometric solutions under ample reduction | [
"Alexander Varchenko"
] | 21 Oct 2020 (<a href="https://arxiv.org/abs/2010.11275v1">v1</a>), last revised 16 Dec 2020 (this version, v2) | Latex, 22 pages, v2: references added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2010.11275 | We consider the KZ differential equations over $\mathbb C$ in the case, when the hypergeometric solutions are one-dimensional integrals. We also consider the same differential equations over a finite field $\mathbb F_p$. We study the polynomial solutions of these differential equations over $\mathbb F_p$, constructed i... | math-33-part-1.zip/2010.11275.pdf |
1310.2168 | Higgs bundles over elliptic curves for complex reductive Lie groups | [
"Emilio Franco",
"Oscar Garcia-Prada",
"P. E. Newstead"
] | 8 Oct 2013 (<a href="https://arxiv.org/abs/1310.2168v1">v1</a>), last revised 17 Apr 2018 (this version, v5) | To appear in Glasgow Mathematical Journal | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1310.2168 | We study Higgs bundles over an elliptic curve with complex reductive structure group, describing the (normalization of) its moduli spaces and the associated Hitchin fibration. The case of trivial degree is covered by the work of Thaddeus in 2001. Our arguments are different from those of Thaddeus and cover arbitrary de... | math-31-part-2.zip/1310.2168.pdf |
1012.2186 | The varieties of tangent lines to hypersurfaces in projective spaces | [
"Atsushi Ikeda"
] | 10 Dec 2010 | 10 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1012.2186 | For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs forms a smooth variety for a general hypersurface. | math-31-part-1.zip/1012.2186.pdf |
math/0411357 | Pole Structure of Topological String Free Energy | [
"Yukiko Konishi"
] | 16 Nov 2004 (<a href="https://arxiv.org/abs/math/0411357v1">v1</a>), last revised 18 Apr 2005 (this version, v3) | 37 pages; v2: materials reorganized and references added, 46 pages; v3:title changed, to appear in Publ. Res. Inst. Math. Sci. Kyoto | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.math/0411357 | We show that the free energy of the topological string admits a certain pole structure by using the operator formalism. Combined with the results of Peng that proved the integrality, this gives a combinatoric proof of the Gopakumar-Vafa conjecture. | math-34-part-1.zip/math_0411357.pdf |
0710.4064 | A Babylonian tower theorem for principal bundles over projective spaces | [
"I. Biswas",
"I. Coanda",
"G. Trautmann"
] | 22 Oct 2007 | 13 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0710.4064 | We generalise the variant of the Babylonian tower theorem for vector bundles on projective spaces proved by I. Coanda and G. Trautmann (2006) to the case of principal $G$-bundles over projective spaces, where $G$ is a linear algebraic group defined over an algebraically closed field. In course of the proofs some new in... | math-31-part-1.zip/0710.4064.pdf |
1001.5433 | Absolute desingularization in characteristic zero | [
"Michael Temkin"
] | 29 Jan 2010 (<a href="https://arxiv.org/abs/1001.5433v1">v1</a>), last revised 28 Aug 2012 (this version, v2) | 26 pages, final version, published in 2011 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1001.5433 | We present a survey on the recent progress with desingularization of quasi-excellent schemes of characteristic zero. Due to expository goals of the paper we concentrate on giving examples and outlining main ideas, and we refer to other sources for detailed proofs and technical details. This survey will be published in ... | math-31-part-1.zip/1001.5433.pdf |
math/0611597 | On the formalisme of mixed sheaves | [
"Morihiko Saito"
] | 20 Nov 2006 | 54 pages, converted from Preprint RIMS-784, Aug. 1991 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0611597 | We give a formalism of mixed sheaves on varieties over a subfield of the complex number field. | math-34-part-2.zip/math_0611597.pdf |
1901.10243 | Motivic measures and $\mathbb{F}_1$-geometries | [
"Lieven Le Bruyn"
] | 29 Jan 2019 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Quantum Algebra (math.QA); Rings and Algebras (math.RA); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1901.10243 | Right adjoints for the forgetful functors on $\lambda$-rings and bi-rings are applied to motivic measures and their zeta functions on the Grothendieck ring of $\mathbb{F}_1$-varieties in the sense of Lorscheid and Lopez-Pena (torified schemes). This leads us to a specific subring of $\mathbb{W}(\mathbb{Z})$, properly c... | math-32-part-2.zip/1901.10243.pdf | |
math/0003033 | Macaulay 2 and the geometry of schemes | [
"Gregory G. Smith",
"Bernd Sturmfels"
] | 5 Mar 2000 | 12 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.math/0003033 | This tutorial illustrates how to use Grayson and Stillman's computer algebra system, Macaulay2, to study schemes. The examples are taken from the homework for an algebraic geometry class given at the University of California, Berkeley in the fall of 1999. This graduate course was taught by the second author with as... | math-34-part-1.zip/math_0003033.pdf |
0907.2503 | The Hodge conjecture for self-products of certain K3 surfaces | [
"Ulrich Schlickewei"
] | 15 Jul 2009 | 24 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0907.2503 | We use a result of van Geemen to determine the endomorphism algebra of the Kuga--Satake variety of a K3 surface with real multiplication. This is applied to prove the Hodge conjecture for self-products of double covers of $\PP^2$ which are ramified along six lines. | math-31-part-1.zip/0907.2503.pdf |
2010.01517 | Noether's problem and rationality problem for multiplicative invariant fields: a survey | [
"Akinari Hoshi"
] | 4 Oct 2020 | 25 pages, Algebraic Number Theory and Related Topics 2016, 29-53, RIMS Kôkyûroku Bessatsu, B77, Res. Inst. Math. Sci. (RIMS), Kyoto, 2020 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2010.01517 | In this paper, we give a brief survey of recent developments on Noether's problem and rationality problem for multiplicative invariant fields including author's recent papers Hoshi [Hos15] about Noether's problem over Q, Hoshi, Kang and Kunyavskii [HKK13], Chu, Hoshi, Hu and Kang [CHHK15], Hoshi [Hos16] and... | math-33-part-1.zip/2010.01517.pdf |
1003.3478 | Algorithms for Checking Rational Roots of $b$-functions and their Applications | [
"Viktor Levandovskyy",
"Jorge Martín-Morales"
] | 17 Mar 2010 | 26 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Symbolic Computation (cs.SC); Rings and Algebras (math.RA) | https://doi.org/10.48550/arXiv.1003.3478 | Bernstein-Sato polynomial of a hypersurface is an important object with numerous applications. It is known, that it is complicated to obtain it computationally, as a number of open questions and challenges indicate. In this paper we propose a family of algorithms called \texttt{checkRoot} for optimized check of whether... | math-31-part-1.zip/1003.3478.pdf |
1707.00752 | Rigid connections and $F$-isocrystals | [
"Hélène Esnault",
"Michael Groechenig"
] | 3 Jul 2017 (<a href="https://arxiv.org/abs/1707.00752v1">v1</a>), last revised 1 Jun 2020 (this version, v4) | final version, accepted in Acta Mathematica | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1707.00752 | An irreducible integrable connection $(E,\nabla)$ on a smooth projective complex variety $X$ is called rigid if it gives rise to an isolated point of the corresponding moduli space $\mathcal{M}_{dR}(X)$. According to Simpson's motivicity conjecture, irreducible rigid flat connections are of geometric origin, that i... | math-32-part-1.zip/1707.00752.pdf |
1608.00423 | Quadric bundles applied to non-maximal Higgs bundles | [
"André Oliveira"
] | 1 Aug 2016 | To appear in the special volume of Travaux Mathématiques dedicated to the GEOQUANT 2015 Conference held at the ICMAT, Madrid; 15 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1608.00423 | We present a survey on the moduli spaces of rank 2 quadric bundles over a compact Riemann surface X. These are objects which generalise orthogonal bundles and which naturally occur through the study of the connected components of the moduli spaces of Higgs bundles over X for the real symplectic group Sp(4,R), with non-... | math-32-part-1.zip/1608.00423.pdf |
0708.1661 | Complex algebraic curves. Annuli | [
"Maciej Borodzik",
"Henryk Zoladek"
] | 13 Aug 2007 | 43 pages. This is the full, unabridged version of our article "Complex algebraic curves via Poincare--Hopf formula. II. Annuli". In this version we include all detailed estimates. The TeX file has been prepared using Scientific Workplace | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0708.1661 | We provide the full classification of algebraic embeddings of $\mathbb{C}^*$ into $\mathbb{C}^2$ satisfying certain regularity condition, which conjecturally holds for all algebraic maps from $\mathbb{C}^*$ into $\mathbb{C}^2$. The resulting list comprises 1 smooth family, 18 discrete families and 4 special cases. Any ... | math-30-part-2.zip/0708.1661.pdf |
0803.0090 | A complex surface of general type with p_g=0, K^2=2 and H_1=Z/2Z, Z/3Z | [
"Yongnam Lee",
"Jongil Park"
] | 2 Mar 2008 (<a href="https://arxiv.org/abs/0803.0090v1">v1</a>), last revised 8 Sep 2008 (this version, v4) | A title is changed and a section is added; 8 pages, 4 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Geometric Topology (math.GT) | https://doi.org/10.48550/arXiv.0803.0090 | As the sequel to [3], we construct a minimal complex surface of general type with p_g=0, K^2=2 and H_1=Z/2Z using a rational blow-down surgery and Q-Gorenstein smoothing theory. We also present an example of p_g = 0,K^2 = 2 and H_1 = Z/3Z. | math-31-part-1.zip/0803.0090.pdf |
1608.04542 | On blowing up the weighted projective plane | [
"Juergen Hausen",
"Simon Keicher",
"Antonio Laface"
] | 16 Aug 2016 | 19 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1608.04542 | We investigate the blow-up of a weighted projective plane at a general point. We provide criteria and algorithms for testing if the result is a Mori dream surface and we compute the Cox ring in several cases. Moreover applications to the study of $\overline{M}_{0,n}$ are discussed. | math-32-part-1.zip/1608.04542.pdf |
math/0602255 | Geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case | [
"Roman Bezrukavnikov",
"Alexander Braverman"
] | 12 Feb 2006 (<a href="https://arxiv.org/abs/math/0602255v1">v1</a>), last revised 4 Dec 2006 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.math/0602255 | Let X be a smooth projective curve over an algebraically closed field k of characteristic p>0. In this paper we explore the relation between algebraic D-modules on the moduli space $Bun_n$ of vector bundles of rank n on X and coherent sheaves on the moduli space $Loc_n$ of vector bundles endowed with a connection (i... | math-34-part-1.zip/math_0602255.pdf | |
1608.00221 | Okounkov bodies associated to pseudoeffective divisors II | [
"Sung Rak Choi",
"Jinhyung Park",
"Joonyeong Won"
] | 31 Jul 2016 (<a href="https://arxiv.org/abs/1608.00221v1">v1</a>), last revised 24 Apr 2017 (this version, v2) | 14 pages, deleted previous Section 5 and fixed several gaps in the previous version. to appear in Taiwanese J. Math. (special issue for the proceedings of the conference Algebraic Geometry in East Asia 2016) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1608.00221 | We first prove some basic properties of Okounkov bodies, and give a characterization of Nakayama and positive volume subvarieties of a pseudoeffective divisor in terms of Okounkov bodies. Next, we show that each valuative and limiting Okounkov bodies of a pseudoeffective divisor which admits the birational good Zariski... | math-32-part-1.zip/1608.00221.pdf |
1705.01382 | Brauer groups of 1-motives | [
"Cristiana Bertolin",
"Federica Galluzzi"
] | 3 May 2017 (<a href="https://arxiv.org/abs/1705.01382v1">v1</a>), last revised 13 Apr 2021 (this version, v5) | final version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1705.01382 | Over a normal base scheme, we prove the generalized Theorem of the Cube for 1-motives and that a torsion class of the group H^2_ét(M,G_m)$ of a 1-motive M, whose pull-back via the unit section is zero, comes from an Azumaya algebra. In particular, we deduce that over an algebraically closed field of characteristic zero... | math-32-part-1.zip/1705.01382.pdf |
1303.1653 | K3 surfaces with a non-symplectic automorphism and product-quotient surfaces with cyclic groups | [
"Alice Garbagnati",
"Matteo Penegini"
] | 7 Mar 2013 | 30 pages, 2 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1303.1653 | We classify all the K3 surfaces which are minimal models of the quotient of the product of two curves $C_1\times C_2$ by the diagonal action of either the group $\Z/p\Z$ or the group $\Z/2p\Z$. These K3 surfaces admit a non-symplectic automorphism of order $p$ induced by an automorphism of one of the curves $C_1$ or $C... | math-31-part-2.zip/1303.1653.pdf |
1905.07126 | On the boundary components of central streams | [
"Nobuhiro Higuchi"
] | 17 May 2019 (<a href="https://arxiv.org/abs/1905.07126v1">v1</a>), last revised 2 Apr 2020 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1905.07126 | Foliations on the space of $p$-divisible groups were studied by Oort in 2004. In his theory, special leaves called central stream play an important role. In this paper, we give a complete classification of the boundary components of the central streams for an arbitrary Newton polygon in the unpolarized case. Hopefully ... | math-32-part-2.zip/1905.07126.pdf | |
2503.12835 | Tropical Poincaré bundle, Fourier-Mukai transform, and a generalized Poincaré formula | [
"Soham Ghosh",
"Farbod Shokrieh"
] | 17 Mar 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.2503.12835 | We construct a tropical analogue of the Poincaré bundle and prove a (cohomological) Fourier-Mukai transform for real tori with integral structures. We then prove a tropical analogue of Beauville's generalized Poincaré formula for polarized abelian varieties. Some consequences include a geometric Riemann-Roch theore... | math-33-part-2.zip/2503.12835.pdf | |
math/0006116 | Virtual Fundamental Classes of Zero Loci | [
"David A. Cox",
"Sheldon Katz",
"Yuan-Pin Lee"
] | 16 Jun 2000 (<a href="https://arxiv.org/abs/math/0006116v1">v1</a>), last revised 6 Dec 2000 (this version, v2) | 11 pages, Latex2e, using amsmath, amsfonts and amsthm packages. This revision includes minor revisions to the text and 4 new references | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0006116 | Let V be a convex vector bundle over a smooth projective manifold X, and let Y be the subset of X which is the zero locus of a regular section of V. This mostly expository paper discusses a conjecture which relates the virtual fundamental classes of X and Y. Using an argument due to Gathmann, we prove a special case of... | math-34-part-1.zip/math_0006116.pdf |
1903.05967 | Asymptotic constructions and invariants of graded linear series | [
"Chih-Wei Chang",
"Shin-Yao Jow"
] | 14 Mar 2019 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1903.05967 | Let $X$ be a complete variety of dimension $n$ over an algebraically closed field $\mathbf{K}$. Let $V_\bullet$ be a graded linear series associated to a line bundle $L$ on $X$, that is, a collection $\{V_m\}_{m\in\mathbb{N}}$ of vector subspaces $V_m\subseteq H^0(X,L^{\otimes m})$ such that $V_0=\mathbf{K}$ and $V_k\c... | math-32-part-2.zip/1903.05967.pdf | |
1410.1585 | The Space of Stability Conditions on Abelian Threefolds, and on some Calabi-Yau Threefolds | [
"Arend Bayer",
"Emanuele Macrì",
"Paolo Stellari"
] | 6 Oct 2014 (<a href="https://arxiv.org/abs/1410.1585v1">v1</a>), last revised 19 Apr 2016 (this version, v2) | 45 pages, 1 figure. v2: addressed referee comments. To appear in Inventiones Math | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1410.1585 | We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following essential steps: <br>1. We simultaneously strengthen a conjecture by the first tw... | math-31-part-2.zip/1410.1585.pdf |
2504.12453 | On generalized Weierstrass Semigroups in arbitrary Kummer extensions of $\mathbb{F}_q(x)$ | [
"Alonso S. Castellanos",
"Erik A. R. Mendoza",
"Guilherme Tizziotti"
] | 16 Apr 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2504.12453 | In this work, we investigate generalized Weierstrass semigroups in arbitrary Kummer extensions of function field $\mathbb{F}_q(x)$. We analyze their structure and properties, with a particular emphasis on their maximal elements. Explicit descriptions of the sets of absolute and relative maximal elements within these se... | math-33-part-2.zip/2504.12453.pdf | |
math/9908093 | Motives and algebraic de rham cohomology | [
"Masanori Asakura"
] | 18 Aug 1999 | Latex2e, to appear | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/9908093 | In this paper, we define a certain Hodge-theoretic structure for an arbitrary variety X over the complex number field by using the theory of mixed Hodge module due to Morihiko Saito. We call it an arithmetic Hodge structure of X. It is shown that extension groups of arithmetic Hodge structure do not vanish even for deg... | math-34-part-2.zip/math_9908093.pdf |
1308.0751 | Sums of squares and varieties of minimal degree | [
"Grigoriy Blekherman",
"Gregory G. Smith",
"Mauricio Velasco"
] | 3 Aug 2013 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1308.0751 | Let X be a real nondegenerate projective subvariety such that its set of real points is Zariski dense. We prove that every real quadratic form that is nonnegative on X is a sum of squares of linear forms if and only if X is a variety of minimal degree. This substantially extends Hilbert's celebrated characterizatio... | math-31-part-2.zip/1308.0751.pdf | |
1709.06923 | Ordered algebraic structures and classification of semifields | [
"Guillaume Tahar"
] | 20 Sep 2017 | 4 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Rings and Algebras (math.RA) | https://doi.org/10.48550/arXiv.1709.06923 | Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For every characteristic, we provide a structure theorem that reduces the classifica... | math-32-part-1.zip/1709.06923.pdf |
math/0308212 | Caractérisation de l'espace projectif | [
"Stéphane Druel"
] | 22 Aug 2003 | 12 pages, in french | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0308212 | The purpose of this paper is to prove the following theorem. Let $X$ be a projective normal variety defined over an algebraically closed field of characteristic zero and let $\Omega_{X}^{1}\to L$ be a one-dimensional foliation on $X$. If $L\cdot C<0$ for all curves $C\subset X$ then either the foliation is regular o... | math-34-part-1.zip/math_0308212.pdf |
1006.0223 | Pfaffian Calabi-Yau Threefolds and Mirror Symmetry | [
"Atsushi Kanazawa"
] | 1 Jun 2010 (<a href="https://arxiv.org/abs/1006.0223v1">v1</a>), last revised 11 Jan 2013 (this version, v4) | 30 pages, to appear in Communications in Number Theory and Physics | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.1006.0223 | The aim of this article is to report on recent progress in understanding mirror symmetry for some non-complete intersection Calabi-Yau threefolds. We first construct four new smooth non-complete intersection Calabi-Yau threefolds with h^{1,1}=1, whose existence was previously conjectured by C. van Enckevort and D. van ... | math-31-part-1.zip/1006.0223.pdf |
2201.03654 | The unreasonable effectiveness of wall-crossing in algebraic geometry | [
"Arend Bayer",
"Emanuele Macrì"
] | 10 Jan 2022 | Contribution to the ICM 2022; 24 pages, 3 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2201.03654 | We survey applications of Bridgeland stability conditions in algebraic geometry and discuss open questions for future research. | math-33-part-1.zip/2201.03654.pdf |
1205.6519 | The Derived Marsden-Weinstein Quotient is Symplectic | [
"Jeremy Pecharich"
] | 29 May 2012 | 8 pages, comments are welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.1205.6519 | Let $(X,\omega_X)$ be a derived scheme with a 0-symplectic form and suppose there is a Hamiltonian $G$-action with a moment map for $G$ a reductive group. We prove, under no further assumptions, that symplectic reduction along any coadjoint orbit in the category of derived Artin stacks has a 0-symplectic form. | math-31-part-2.zip/1205.6519.pdf |
2307.15416 | Class field theory for curves over local fields | [
"Amalendu Krishna",
"Subhadip Majumder"
] | 28 Jul 2023 | 46 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2307.15416 | We establish a ramified class field theory for smooth projective curves over local fields. As key steps in the proof, we obtain new results in the class field theory for 2-dimensional local fields of positive characteristic, and prove a duality theorem for the logarithmic Hodge-Witt cohomology on affine curves over loc... | math-33-part-2.zip/2307.15416.pdf |
math/0511700 | Local structure of abelian covers | [
"Donatella Iacono"
] | 29 Nov 2005 (<a href="https://arxiv.org/abs/math/0511700v1">v1</a>), last revised 2 Jun 2006 (this version, v2) | Revised version; latex: 12 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.math/0511700 | We study normal finite abelian covers of smooth varieties. In particular we establish combinatorial conditions so that a normal finite abelian cover of a smooth variety is Gorenstein or locally complete intersection. | math-34-part-1.zip/math_0511700.pdf |
0802.3669 | A cascade of determinantal Calabi--Yau threefolds | [
"Grzegorz Kapustka",
"Michal Kapustka"
] | 25 Feb 2008 (<a href="https://arxiv.org/abs/0802.3669v1">v1</a>), last revised 17 Mar 2009 (this version, v3) | corrected hodge numbers of two families | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0802.3669 | We study Kustin--Miller unprojections of Calabi--Yau threefolds. As an application we work out the geometric properties of Calabi--Yau threefolds defined as linear sections of determinantal varieties. We compute their Hodge numbers and describe the morphisms corresponding to the faces of their Kähler--Mori cone. | math-31-part-1.zip/0802.3669.pdf |
0901.4400 | Faster Real Feasibility via Circuit Discriminants | [
"Frederic Bihan",
"J. Maurice Rojas",
"Casey Stella"
] | 28 Jan 2009 (<a href="https://arxiv.org/abs/0901.4400v1">v1</a>), last revised 29 Jan 2009 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Computational Complexity (cs.CC); Optimization and Control (math.OC) | https://doi.org/10.48550/arXiv.0901.4400 | We show that detecting real roots for honestly n-variate (n+2)-nomials (with integer exponents and coefficients) can be done in time polynomial in the sparse encoding for any fixed n. The best previous complexity bounds were exponential in the sparse encoding, even for n fixed. We then give a characterization of those ... | math-31-part-1.zip/0901.4400.pdf | |
1609.08797 | A note about connectedness theorems a la Barth | [
"Robert Laterveer"
] | 28 Sep 2016 | To appear (in slightly different form) in Geom. Dedicata. 11 pages, comments very welcome ! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1609.08797 | We prove Barth-type connectedness results for low-codimension smooth subvarieties with good numerical properties inside certain "easy" ambient spaces (such as homogeneous varieties, or spherical varieties). The argument employs some basics from the theory of cones of cycle classes, in particular the notion of b... | math-32-part-1.zip/1609.08797.pdf |
2001.11084 | Hypertoric Hitchin systems and Kirchhoff polynomials | [
"Michael Groechenig",
"Michael McBreen"
] | 29 Jan 2020 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2001.11084 | We define a formal algebraic analogue of hypertoric Hitchin systems, whose complex-analytic counterparts were defined by Hausel-Proudfoot. These are algebraic completely integrable systems associated to a graph. We study the variation of the Tamagawa number of the resulting family of abelian varieties, and show that it... | math-32-part-2.zip/2001.11084.pdf | |
2407.21288 | On the derived category of a toric stack bundle | [
"Qian Chao",
"Jiun-Cheng Chen",
"Hsian-Hua Tseng"
] | 31 Jul 2024 (<a href="https://arxiv.org/abs/2407.21288v1">v1</a>), last revised 11 Jan 2025 (this version, v2) | v1: 7 pages. v2: 7 pages, small corrections, to appear in Journal of Pure and Applied Algebra | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2407.21288 | We establish some properties of the derived category of torus-equivariant coherent sheaves on a split toric stack bundle. Our main result is a semi-orthogonal decomposition of such a category. | math-33-part-2.zip/2407.21288.pdf |
0810.0141 | Smoothing nodal Calabi-Yau n-folds | [
"S. Rollenske",
"R. P. Thomas"
] | 1 Oct 2008 (<a href="https://arxiv.org/abs/0810.0141v1">v1</a>), last revised 3 Dec 2019 (this version, v3) | Included missing torsion in Lemma 2.5. Results unchanged. 20 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Differential Geometry (math.DG) | https://doi.org/10.48550/arXiv.0810.0141 | Let X be an n-dimensional Calabi-Yau with ordinary double points, where n is odd. Friedman showed that for n=3 the existence of a smoothing of X implies a specific type of relation between homology classes on a resolution of X. (The converse is also true, due to work of Friedman, Kawamata and Tian.) <br>We sketch a mor... | math-31-part-1.zip/0810.0141.pdf |
1607.05469 | Stability of Rank 2 Ulrich Bundles on Projective K3 Surfaces | [
"Gianfranco Casnati",
"Federica Galluzzi"
] | 19 Jul 2016 (<a href="https://arxiv.org/abs/1607.05469v1">v1</a>), last revised 9 Oct 2016 (this version, v2) | 14 pages. Comments welcome. The final version of the article is published in Mathematica Scandinavica | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1607.05469 | Let $F\subseteq\mathbb P ^{a+1}$ be a non-degenerate $K3$ surface of degree $2a$, where $a\ge2$. In this paper we deal with Ulrich bundles on $F$ of rank $2$. We deal with their stability and we construct $K3$ surfaces endowed with families of non-special Ulrich bundles of rank $2$ for each $a\ge2$. | math-32-part-1.zip/1607.05469.pdf |
1905.01936 | Rational cubic fourfolds in Hassett divisors | [
"Song Yang",
"Xun Yu"
] | 6 May 2019 | 10 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1905.01936 | We prove that every Hassett's Noether-Lefschetz divisor of special cubic fourfolds contains a union of three codimension-two subvarieties, parametrizing rational cubic fourfolds, in the moduli space of smooth cubic fourfolds. | math-32-part-2.zip/1905.01936.pdf |
2011.14658 | LG/CY correspondence between $tt^*$ geometries | [
"Huijun Fan",
"Tian Lan",
"Zongrui Yang"
] | 30 Nov 2020 | 41 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.2011.14658 | The concept of $tt^*$ geometric structure was introduced by physicists (see \cite{CV1, BCOV} and references therein) , and then studied firstly in mathematics by C. Hertling \cite{Het1}. It is believed that the $tt^*$ geometric structure contains the whole genus $0$ information of a two dimensional topological field th... | math-33-part-1.zip/2011.14658.pdf |
1108.0164 | Depth of characters of curve complements and orbifold pencils | [
"E. Artal Bartolo",
"J.I. Cogolludo-Agustin",
"A. Libgober"
] | 31 Jul 2011 | 21 pages, 1 picture | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1108.0164 | The present work is a user's guide to the results of a previous paper by the second and third authors, where a description of the space of characters of a quasi-projective variety was given in terms of global quotient orbifold pencils. <br>Below we consider the case of plane curve complements and hyperplane arrange... | math-31-part-1.zip/1108.0164.pdf |
math/0303189 | Log-terminal singularities and vanishing theorems | [
"Hans Schoutens"
] | 15 Mar 2003 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Rings and Algebras (math.RA) | https://doi.org/10.48550/arXiv.math/0303189 | Generalizing work of Smith and Hara, we give a new characterization of log-terminal singularities for finitely generated algebras over $\mathbb C$, in terms of purity properties of ultraproducts of characteristic $p$ Frobenii. <br>The first application is a Boutôt-type theorem for log-terminal singularities: given a pu... | math-34-part-1.zip/math_0303189.pdf | |
alg-geom/9612007 | Intermediate Jacobians of moduli spaces | [
"Donu Arapura",
"Pramathanath Sastry"
] | 7 Dec 1996 | AMS-LaTeX, 16 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9612007 | Let $SU_X(n,L)$ be the moduli space of rank n semistable vector bundles with fixed determinant L on a smooth projective genus g curve X. Let $SU_X^s(n,L)$ denote the open subset parametrizing stable bundles. We show that if g>3 and n > 1, then the mixed Hodge structure on $H^3(SU_X^s(n, L))$ is pure of type ${(1,... | small_categories-00.zip/alg-geom_9612007.pdf |
1303.2241 | Classification of polarized symplectic automorphisms of Fano varieties of cubic fourfolds | [
"Lie Fu"
] | 9 Mar 2013 (<a href="https://arxiv.org/abs/1303.2241v1">v1</a>), last revised 13 Mar 2013 (this version, v2) | 21 pages. Comments are welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1303.2241 | We classify the polarized symplectic automorphisms of Fano varieties of smooth cubic fourfolds (equipped with the Plücker polarization) and study the fixed loci. | math-31-part-2.zip/1303.2241.pdf |
1808.06345 | Pseudolattices, del Pezzo surfaces, and Lefschetz fibrations | [
"Andrew Harder",
"Alan Thompson"
] | 20 Aug 2018 (<a href="https://arxiv.org/abs/1808.06345v1">v1</a>), last revised 28 Jul 2019 (this version, v2) | v2: Minor revisions at the request of the referee. Remark 3.24 is new, as is the discussion of the noncommutative setting in the final section | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.1808.06345 | Motivated by the relationship between numerical Grothendieck groups induced by the embedding of a smooth anticanonical elliptic curve into a del Pezzo surface, we define the notion of a quasi del Pezzo homomorphism between pseudolattices and establish its basic properties. The primary aim of the paper is then to prove ... | math-32-part-2.zip/1808.06345.pdf |
0805.4634 | The perverse filtration and the Lefschetz Hyperplane Theorem | [
"Mark Andrea de Cataldo",
"Luca Migliorini"
] | 29 May 2008 (<a href="https://arxiv.org/abs/0805.4634v1">v1</a>), last revised 6 Jan 2009 (this version, v2) | Revised version with minor changes. To appear in Annals of Mathematics | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0805.4634 | We describe the perverse filtration in cohomology using the Lefschetz Hyperplane Theorem. | math-31-part-1.zip/0805.4634.pdf |
math/0410526 | Arcs, valuations and the Nash map | [
"Shihoko Ishii"
] | 25 Oct 2004 (<a href="https://arxiv.org/abs/math/0410526v1">v1</a>), last revised 23 Feb 2005 (this version, v2) | One wrong statement in Theorem 3.6 was deleted. This does not affect the rest of this paper | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0410526 | This paper gives a map from the set of families of arcs on a variety to the set of valuations on the rational function field of the variety We characterize a family of arcs which corresponds to a divisorial valuation by this map. We can see that both the Nash map and a certain McKay correspondence are the restrictions ... | math-34-part-1.zip/math_0410526.pdf |
2503.04383 | Generalized Brieskorn Modules II: Higher Bernstein Polynomials and Multiple Poles | [
"Daniel Barlet"
] | 6 Mar 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.2503.04383 | Our main result is to show that the existence of a root in. --$\alpha$--Nfor the p-th Bernstein polynomial of the (a,b)-module generated by a holomorphicform in the (convergent) Brieskorn (a,b)-module associated to f, under the hypothesis that f has an isolated singularity at the origin relative to the eigenvalue exp(2... | math-33-part-2.zip/2503.04383.pdf | |
2103.08779 | On the structure of a log smooth pair in the equality case of the Bogomolov-Gieseker inequality | [
"Masataka Iwai"
] | 16 Mar 2021 (<a href="https://arxiv.org/abs/2103.08779v1">v1</a>), last revised 2 Dec 2022 (this version, v3) | 14pages, v3: completely revised version, to appear in Annales de l'Institut Fourier | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV); Differential Geometry (math.DG) | https://doi.org/10.48550/arXiv.2103.08779 | We study the structure of a log smooth pair when the equality holds in the Bogomolov-Gieseker inequality for the logarithmic tangent bundle and this bundle is semistable with respect to some ample divisor. We also study the case of the canonical extension sheaf. | math-33-part-1.zip/2103.08779.pdf |
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