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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2003.00096 | A Recursive Formula for Osculating Curves | [
"Giosuè Muratore"
] | 28 Feb 2020 (<a href="https://arxiv.org/abs/2003.00096v1">v1</a>), last revised 2 Aug 2024 (this version, v3) | Notation, small modification in Introduction, Prop. 4.1 and Lemma 5.2 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2003.00096 | Let $X$ be a smooth complex projective variety. Using a construction devised to Gathmann, we present a recursive formula for some of the Gromov-Witten invariants of $X$. We prove that, when $X$ is homogeneous, this formula gives the number of osculating rational curves at a general point of a general hypersurface of $X... | math-32-part-2.zip/2003.00096.pdf |
1802.07032 | A remark on the Chow ring of Sicilian surfaces | [
"Robert Laterveer"
] | 20 Feb 2018 | To appear in Comment. Math. Univ. St. Pauli, 9 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1802.07032 | We propose a "Bloch type" conjecture for surfaces: if the cup product map in coherent cohomology is zero, then all intersections of homologically trivial divisors should be zero in the Chow group of zero-cycles. We prove this conjecture for Sicilian surfaces. | math-32-part-2.zip/1802.07032.pdf |
2403.10712 | Jacobian elliptic fibrations on K3s with a non-symplectic automorphism of order 3 | [
"Felipe Zingali Meira"
] | 15 Mar 2024 (<a href="https://arxiv.org/abs/2403.10712v1">v1</a>), last revised 13 Jun 2024 (this version, v2) | 37 pages, 6 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2403.10712 | We classify Jacobian elliptic fibrations on K3 surfaces with a non-symplectic automorphism $\sigma$ of order 3 according to the action of $\sigma$ on their fibres, building on work by Garbagnati and Salgado for non-symplectic involutions. We determine the possible reducible fibres types and give Weierstrass equations f... | math-33-part-2.zip/2403.10712.pdf |
alg-geom/9206004 | Extremal Rays and Null Geodesics on a Complex Conformal Manifold | [
"Yun-Gang Ye"
] | 11 Jun 1992 (<a href="https://arxiv.org/abs/alg-geom/9206004v1">v1</a>), last revised 30 Jun 1992 (this version, v2) | 17 pages, AMS-TeX version 2.1 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9206004 | This is a revised version of the paper submitted before. | small_categories-00.zip/alg-geom_9206004.pdf |
1205.4742 | Riemann-Roch for Deligne-Mumford stacks | [
"Dan Edidin"
] | 21 May 2012 (<a href="https://arxiv.org/abs/1205.4742v1">v1</a>), last revised 12 Nov 2012 (this version, v2) | 30 pages, to appear in proceedings of the Harris 60 conference | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); K-Theory and Homology (math.KT) | https://doi.org/10.48550/arXiv.1205.4742 | We give a simple proof of the Riemann-Roch theorem for Deligne-Mumford stacks using the equivariant Riemann-Roch theorem and the localization theorem in equivariant K-theory together with some basic commutative algebra of Artin rings. | math-31-part-2.zip/1205.4742.pdf |
2404.16172 | Mirror Construction for Nakajima Quiver Varieties | [
"Jiawei Hu",
"Siu-Cheong Lau",
"Ju Tan"
] | 24 Apr 2024 (<a href="https://arxiv.org/abs/2404.16172v1">v1</a>), last revised 19 Dec 2024 (this version, v3) | Improved exposition. Comments are welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.2404.16172 | In this paper, we construct the ADHM quiver representations and the corresponding sheaves as the mirror objects of formal deformations of the framed immersed Lagrangian sphere decorated with flat bundles. More generally, we construct Nakajima quiver varieties as localized mirrors of framed nodal unions of Lagrangian sp... | math-33-part-2.zip/2404.16172.pdf |
1510.05622 | Sparse Polynomial Systems with many Positive Solutions from Bipartite Simplicial Complexes | [
"Frédéric Bihan",
"Pierre-Jean Spaenlehauer"
] | 19 Oct 2015 (<a href="https://arxiv.org/abs/1510.05622v1">v1</a>), last revised 18 Apr 2016 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Symbolic Computation (cs.SC) | https://doi.org/10.48550/arXiv.1510.05622 | Consider a regular triangulation of the convex-hull $P$ of a set $\mathcal A$ of $n$ points in $\mathbb R^d$, and a real matrix $C$ of size $d \times n$. A version of Viro's method allows to construct from these data an unmixed polynomial system with support $\mathcal A$ and coefficient matrix $C$ whose number of p... | math-32-part-1.zip/1510.05622.pdf | |
2403.17681 | A Wall Crossing Formula for Motivic Enumerative Invariants | [
"Andrés Jaramillo Puentes"
] | 26 Mar 2024 (<a href="https://arxiv.org/abs/2403.17681v1">v1</a>), last revised 4 Feb 2025 (this version, v3) | 16 pages, 6 figures; Corrected typos | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2403.17681 | We prove an analog of the wall crossing formula for Welschinger invariants relating the difference of signed curve counting of real curves passing through configurations that differ by a pair of complex conjugated points, and a correspondence Welschinger invariant of the blow up. <br>We prove this analogue for the moti... | math-33-part-2.zip/2403.17681.pdf |
1905.04055 | On the Hilbert vector of the Jacobian module of a plane curve | [
"Armando Cerminara",
"Alexandru Dimca",
"Giovanna Ilardi"
] | 10 May 2019 (<a href="https://arxiv.org/abs/1905.04055v1">v1</a>), last revised 28 Jan 2020 (this version, v2) | 10 pages, 4 figures. To appear in Portugaliae Mathematica | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1905.04055 | We identify several classes of curves $C:f=0$, for which the Hilbert vector of the Jacobian module $N(f)$ can be completely determined, namely the 3-syzygy curves, the maximal Tjurina curves and the nodal curves, having only rational irreducible components. A result due to Hartshorne, on the cohomology of some rank 2 v... | math-32-part-2.zip/1905.04055.pdf |
0707.3947 | A computation of invariants of a rational self-map | [
"Ekaterina Amerik"
] | 26 Jul 2007 | LaTeX, 10 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0707.3947 | I compute the dynamical degrees in C. Voisin's example of a rational self-map of the variety of lines on a cubic fourfold. | math-30-part-2.zip/0707.3947.pdf |
1608.06742 | $D$-modules and finite monodromy | [
"Hélène Esnault",
"Mark Kisin"
] | 24 Aug 2016 (<a href="https://arxiv.org/abs/1608.06742v1">v1</a>), last revised 3 Sep 2016 (this version, v2) | 9 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1608.06742 | We investigate an analogue of the Grothendieck $p$-curvature conjecture, where the vanishing of the $p$-curvature is replaced by the stronger condition, that the module with connection mod $p$ underlies a $\mathcal{D}_X$-module structure. We show that this weaker conjecture holds in various situations, for example if t... | math-32-part-1.zip/1608.06742.pdf |
1811.11086 | Geometric models for fibrant resolutions of motivic suspension spectra | [
"Andrei Druzhinin"
] | 27 Nov 2018 (<a href="https://arxiv.org/abs/1811.11086v1">v1</a>), last revised 29 Nov 2018 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1811.11086 | We construct geometric models for the $\mathbb P^1$-spectrum $M_{\mathbb P^1}(Y)$, which computes in Garkusha-Panin's theory of framed motives \cite{GP14} a positively motivically fibrant $\Omega_{\mathbb P^1}$ replacement of $\Sigma_{\mathbb P^1}^\infty Y$ for a smooth scheme $Y\in \Sm_k$ over a perfect field $k$.... | math-32-part-2.zip/1811.11086.pdf | |
1104.4840 | Inversion of subadjunction and multiplier ideals | [
"Eugene Eisenstein"
] | 26 Apr 2011 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1104.4840 | We present a generalization of the multiplier ideal version of inversion of adjunction, often known as the restriction theorem, to centers of arbitrary codimension. We approach inversion of adjunction from the subadjunction point of view. Let X be a smooth complex projective variety and let Z be an exceptional log-cano... | math-31-part-1.zip/1104.4840.pdf | |
2002.12049 | Weight Spaces and Attracting Sets for Torus Actions on Quiver Moduli | [
"Magdalena Boos",
"Hans Franzen"
] | 27 Feb 2020 | Comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.2002.12049 | We study torus actions on moduli spaces of quivers. First we give a description of the weight spaces of the induced action of the tangent space to a torus-fixed point. Then we focus on actions of tori of rank one and derive an explicit form for the attractors in the Białynicki-Birula decomposition. | math-32-part-2.zip/2002.12049.pdf |
1004.0122 | Resonance webs of hyperplane arrangements | [
"Jorge Vitorio Pereira"
] | 1 Apr 2010 (<a href="https://arxiv.org/abs/1004.0122v1">v1</a>), last revised 25 Nov 2010 (this version, v2) | (v2) Minor changes following suggestions of the referee. To appear in the Proceedings of the 2nd MSJ-SI on Arrangements of Hyperplanes | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.1004.0122 | Each irreducible component of the first resonance variety of a hyperplane arrangement naturally determines a codimension one foliation on the ambient space. The superposition of these foliations define what we call the resonance web of the arrangement. In this paper we initiate the study of these objects with emphasis ... | math-31-part-1.zip/1004.0122.pdf |
1503.00112 | Transcendental Morse Inequality and Generalized Okounkov Bodies | [
"Ya Deng"
] | 28 Feb 2015 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1503.00112 | The main goal of this article is to construct "arithmetic Okounkov bodies" for an arbitrary pseudo-effective (1,1)-class $\alpha$ on a Kähler manifold. Firstly, using Boucksom's divisorial Zariski decompositions for pseudo-effective (1,1)-classes on compact Kähler manifolds, we prove the differentiability o... | math-32-part-1.zip/1503.00112.pdf | |
1707.08611 | Étale Covers and Local Algebraic Fundamental Groups | [
"Charlie Stibitz"
] | 26 Jul 2017 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1707.08611 | Let $X$ be a normal noetherian scheme and $Z \subseteq X$ a closed subset of codimension $\geq 2$. We consider here the local obstructions to the map $\hat{\pi}_{1}(X\backslash Z) \to \hat{\pi}_{1}(X)$ being an isomorphism. Assuming $X$ has a regular alteration, we prove the equivalence of the obstructions being finite... | math-32-part-1.zip/1707.08611.pdf | |
1412.8499 | An Introduction to Hodge Structures | [
"Sara Angela Filippini",
"Helge Ruddat",
"Alan Thompson"
] | 29 Dec 2014 (<a href="https://arxiv.org/abs/1412.8499v1">v1</a>), last revised 16 Jan 2015 (this version, v2) | 38 pages, 2 figures. To appear in Lecture Notes of the Concentrated Graduate Courses for Calabi-Yau Varieties: Arithmetic, Geometry and Physics; forthcoming volume in the Fields Institute Communications Series. v2: Edited to correct a problem with theorem numbering in the original submission | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1412.8499 | We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kahler manifolds to the families of Hodge structures defined on their cohomology, and discuss its properties. This wi... | math-31-part-2.zip/1412.8499.pdf |
math/0505482 | A Compactification of the Space of Holomorphic Maps from $¶^1$ into $¶^r$ | [
"Jiayuan Lin"
] | 23 May 2005 (<a href="https://arxiv.org/abs/math/0505482v1">v1</a>), last revised 25 May 2005 (this version, v2) | 25 pages, typos corrected, more precise reference added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0505482 | Let $M_{d}(¶^r)$ be the space of $(r+1)$-tuples $(f_0,...,f_r)$ modulo homothety, where $f_0,...,f_r$ are homogeneous polynomials of degree $d$ in two variables. Let $M_{d}^{\circ}(¶^r)$ be the open subset of $M_{d}(¶^r)$ such that $f_0,...,f_r$ have no common zeros. Then $M_{d}^{\circ}(¶^r)$ parametrizes the space of ... | math-34-part-1.zip/math_0505482.pdf |
1004.4379 | A generalization of Fulton's conjecture for arbitrary groups | [
"Prakash Belkale",
"Shrawan Kumar",
"Nicolas Ressayre"
] | 25 Apr 2010 | 20 pages, no figures. | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1004.4379 | We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory. | math-31-part-1.zip/1004.4379.pdf |
math/0510499 | Even sets of nodes on sextic surfaces | [
"Fabrizio Catanese",
"Fabio Tonoli"
] | 24 Oct 2005 | 44 pages, including two Macaulay Scripts | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.math/0510499 | We determine the possible even sets of nodes on sextic surfaces in $\Pn 3$, showing in particular that their cardinalities are exactly the numbers in the set $\{24, 32, 40, 56 \}$. We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and proje... | math-34-part-1.zip/math_0510499.pdf |
1801.01779 | Logarithmic de Rham comparison for open rigid spaces | [
"Shizhang Li",
"Xuanyu Pan"
] | 5 Jan 2018 (<a href="https://arxiv.org/abs/1801.01779v1">v1</a>), last revised 2 Feb 2020 (this version, v3) | Add references. 39 pages, comments welcome v2: final version, 40 pages, comments still welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1801.01779 | In this note, we prove the logarithmic $p$-adic comparison theorem for open rigid analytic varieties. We prove that a smooth rigid analytic variety with a strict simple normal crossing divisor is locally $K(\pi,1)$ (in a certain sense) with respect to $\mathbb{F}_p$-local systems and ramified coverings along the diviso... | math-32-part-2.zip/1801.01779.pdf |
2101.01446 | The Balmer spectrum of certain Deligne-Mumford stacks | [
"Eike Lau"
] | 5 Jan 2021 (<a href="https://arxiv.org/abs/2101.01446v1">v1</a>), last revised 5 Oct 2022 (this version, v2) | major revision, main result improved (no regularity assumption) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.2101.01446 | We consider a Deligne-Mumford stack $X$ which is the quotient of an affine scheme $\operatorname{Spec}A$ by the action of a finite group $G$ and show that the Balmer spectrum of the tensor triangulated category of perfect complexes on $X$ is homeomorphic to the space of homogeneous prime ideals in the group cohomology ... | math-33-part-1.zip/2101.01446.pdf |
2205.05288 | Anticanonical volume of Fano 4-folds | [
"Caucher Birkar"
] | 11 May 2022 (<a href="https://arxiv.org/abs/2205.05288v1">v1</a>), last revised 19 Sep 2022 (this version, v2) | V2: minor corrections applied, 8 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2205.05288 | We find an explicit upper bound for the anticanonical volume of Fano 4-folds with canonical singularities. | math-33-part-1.zip/2205.05288.pdf |
1311.1261 | Hopf algebraic techniques applied to super algebraic groups | [
"Akira Masuoka"
] | 6 Nov 2013 (<a href="https://arxiv.org/abs/1311.1261v1">v1</a>), last revised 3 Jan 2017 (this version, v2) | Corrected typos on Page 2, line 13 and on Page 9, line 14, adding Footnote 5 for the latter; corrected Condition 2 of Lemma 7.3; Up-dated the References | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1311.1261 | Reproducing my talk at Algebra Symposium held at Hiroshima University, August 26--29, 2013, I review recent results on super algebraic groups, emphasizing results obtained by myself and my coauthors using Hopf algebraic techniques. The results are all basic, and I intend to make this report into a somewhat informal int... | math-31-part-2.zip/1311.1261.pdf |
2502.16956 | Jordan property for automorphism groups of compact varieties | [
"Yujie Luo",
"Sheng Meng",
"De-Qi Zhang"
] | 24 Feb 2025 (<a href="https://arxiv.org/abs/2502.16956v1">v1</a>), last revised 22 Aug 2025 (this version, v2) | 21 pages; minor editing; EMS Surveys in Mathematical Sciences (to appear) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Group Theory (math.GR) | https://doi.org/10.48550/arXiv.2502.16956 | In this note, we report some recent progress on the Jordan property for (birational) automorphism groups of projective varieties and compact complex varieties. | math-33-part-2.zip/2502.16956.pdf |
math/9904049 | Polydiagonal compactification of configuration spaces | [
"Alexander Ulyanov"
] | 12 Apr 1999 (<a href="https://arxiv.org/abs/math/9904049v1">v1</a>), last revised 23 May 2000 (this version, v2) | 28 pages, 12 figures, AMSLaTeX, xypic Version 2: improved exposition, more pictures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/9904049 | A smooth compactification X<n> of the configuration space of n distinct labeled points in a smooth algebraic variety X is constructed by a natural sequence of blowups, with the full symmetry of the permutation group S_n manifest at each stage of the construction. The strata of the normal crossing divisor at infin... | math-34-part-2.zip/math_9904049.pdf |
1002.3520 | Topological flatness of local models for ramified unitary groups. I. The odd dimensional case | [
"Brian D. Smithling"
] | 18 Feb 2010 (<a href="https://arxiv.org/abs/1002.3520v1">v1</a>), last revised 27 Sep 2010 (this version, v2) | Minor revisions, some of which incorporate suggestions of the referee. 27 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO); Group Theory (math.GR) | https://doi.org/10.48550/arXiv.1002.3520 | Local models are certain schemes, defined in terms of linear-algebraic moduli problems, which give étale-local neighborhoods of integral models of certain p-adic PEL Shimura varieties defined by Rapoport and Zink. When the group defining the Shimura variety ramifies at p, the local models (and hence the Shimura models)... | math-31-part-1.zip/1002.3520.pdf |
1607.04181 | Projective completions of graded unipotent quotients | [
"Gergely Bérczi",
"Brent Doran",
"Thomas Hawes",
"Frances Kirwan"
] | 14 Jul 2016 (<a href="https://arxiv.org/abs/1607.04181v1">v1</a>), last revised 21 Jan 2020 (this version, v3) | With an Appendix by Eloise Hamilton; Revised version, 74 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1607.04181 | The aim of this paper is to show that classical geometric invariant theory (GIT) has an effective analogue for linear actions of a non-reductive algebraic group $H$ with graded unipotent radical on a projective scheme $X$. Here the linear action of $H$ is required to extend to a semi-direct product $\hat{H} = H \rtimes... | math-32-part-1.zip/1607.04181.pdf |
2006.13034 | The Norm map on the compactified Jacobian, the Prym stack and Spectral data for G-Higgs pairs | [
"Raffaele Carbone"
] | 22 Jun 2020 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2006.13034 | This thesis, done under the supervision of Filippo Viviani, is devoted to the study of the spectral correspondence for $G$-Higgs pairs, in the case of $G=SL(r,\mathbb{C})$, $PGL(r, \mathbb{C})$, $Sp(2r,\mathbb{C})$, $GSp(2r,\mathbb{C})$, $PSp(2r,\mathbb{C})$, over any fiber. <br>In the first chapter we introduce the co... | math-33-part-1.zip/2006.13034.pdf | |
2209.03667 | Wall divisors on irreducible symplectic orbifolds of Nikulin-type | [
"Grégoire Menet",
"Ulrike Riess"
] | 8 Sep 2022 | 38 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2209.03667 | We determine the wall divisors on irreducible symplectic orbifolds which are deformation equivalent to a special type of examples, called Nikulin orbifolds. The Nikulin orbifolds are obtained as partial resolutions in codimension 2 of a quotient by a symplectic involution of a Hilbert scheme of 2 points on a K3 surface... | math-33-part-1.zip/2209.03667.pdf |
1305.4435 | Software for multiplier ideals | [
"Zach Teitler"
] | 20 May 2013 | 7 pages. Comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.1305.4435 | We describe a new software package for computing multiplier ideals in certain cases, including monomial ideals, monomial curves, generic determinantal ideals, and hyperplane arrangements. In these cases we take advantage of combinatorial formulas for multiplier ideals given by results of Howald, Thompson, and Johnson. ... | math-31-part-2.zip/1305.4435.pdf |
1303.5578 | Affine ADE bundles over complex surfaces with p_g=0 | [
"Yunxia Chen",
"Naichung Conan Leung"
] | 22 Mar 2013 | 22pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1303.5578 | We study simply-laced simple affine Lie algebra bundles over complex surfaces X. Given any Kodaira curve C in X, we construct such a bundle over X. After deformations, it becomes trivial on every irreducible component of C provided that p_g(X)=0. When X is a blowup of P^2 at nine points, there is a canonical E_8-bundle... | math-31-part-2.zip/1303.5578.pdf |
2308.03394 | On numerically trivial automorphisms of compact hyperkähler manifolds of dimension 4 | [
"Chen Jiang",
"Wenfei Liu"
] | 7 Aug 2023 (<a href="https://arxiv.org/abs/2308.03394v1">v1</a>), last revised 25 May 2024 (this version, v2) | 10 pages, final version to appear in Math. Res. Lett | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2308.03394 | We prove that the automorphism group of a compact hyperkähler manifold of dimension 4 acts faithfully on the cohomology ring. | math-33-part-2.zip/2308.03394.pdf |
2312.17656 | Canonical mirror models for maximal orthogonal Grassmannians | [
"Peter Spacek",
"Charles Wang"
] | 29 Dec 2023 | 6 pages, contribution to the proceedings of the 15th international workshop "Lie Theory and its Applications in Physics" (June 2023) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.2312.17656 | In this report we use our methods in <a href="https://arxiv.org/abs/2204.03548" data-arxiv-id="2204.03548" class="link-https">arXiv:2204.03548</a> and its upcoming generalization to complete the construction of canonical mirror models for all cominuscule homogeneous spaces, by considering the maximal orthogonal Grassma... | math-33-part-2.zip/2312.17656.pdf |
0804.1023 | Submanifolds with ample normal bundles and a conjecture of Hartshorne | [
"Thomas Peternell"
] | 7 Apr 2008 | 14 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.0804.1023 | The Hartshorne conjecture predicts that two submanifolds X and Y in a projective manifold Z with ample normal bundles meets as soon as dim X + dim Y is at least dim Z. We mostly assume slightly stronger that one of the normal bundles is positive in the sense of Griffiths. We observe that the conjecture holds genericall... | math-31-part-1.zip/0804.1023.pdf |
1512.05880 | Motivic and derived motivic Hirzebruch classes | [
"Jean-Paul Brasselet",
"Joerg Schuermann",
"Shoji Yokura"
] | 18 Dec 2015 (<a href="https://arxiv.org/abs/1512.05880v1">v1</a>), last revised 20 Mar 2016 (this version, v3) | 19 pages, comments are welcome: we have made some revisions; to appear in Homology, Homotopy and Applications | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.1512.05880 | In this paper we give a formula for the Hirzebruch $\chi_y$-genus $\chi_y(X)$ and similarly for the motivic Hirzebruch class $T_{y*}(X)$ for possibly singular varieties $X$, using the Vandermonde matrix. Motivated by the notion of secondary Euler characteristic and higher Euler characteristic, we consider a similar not... | math-32-part-1.zip/1512.05880.pdf |
math/0102152 | Polar Homology and Holomorphic Bundles | [
"B. Khesin",
"A. Rosly"
] | 19 Feb 2001 | 16 pages; expanded version of the talk given by one of the authors at the discussion meeting "Topological methods in the physical sciences" London, Nov. 15-16, 2000; to appear in Philos. Trans. Roy. Soc. London Ser. A | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.math/0102152 | We describe polar homology groups for complex manifolds. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincare residue on it. The polar homology groups may be regarded as holomorphic analogues of the... | math-34-part-1.zip/math_0102152.pdf |
2112.02907 | Espaces de Berkovich sur $\mathbb{Z}$: morphismes étales | [
"Dorian Berger"
] | 6 Dec 2021 (<a href="https://arxiv.org/abs/2112.02907v1">v1</a>), last revised 12 Jan 2022 (this version, v2) | in French | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2112.02907 | We develop properties of unramified, étale and smooth morphisms between Berkovich spaces over $\mathbb{Z}$. We prove that they satisfy properties analogous to those of morphisms of schemes and we provide analytification criteria. Our results hold for any valued field, rings of integers of a number field and discrete va... | math-33-part-1.zip/2112.02907.pdf |
1310.1303 | A counterexample concerning quantifier elimination in quasianalytic structures | [
"Krzysztof Jan Nowak"
] | 4 Oct 2013 (<a href="https://arxiv.org/abs/1310.1303v1">v1</a>), last revised 20 May 2014 (this version, v4) | 16 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Functional Analysis (math.FA) | https://doi.org/10.48550/arXiv.1310.1303 | This paper is a revised version of our preprints IMUJ Preprint 2012/04 and RAAG Preprint 343 from May 2012. It provides an example of a quasianalytic structure which, unlike the classical analytic structure, does not admit quantifier elimination in the language of restricted quasianalytic functions augmented by the rec... | math-31-part-2.zip/1310.1303.pdf |
1202.5177 | On the multiplicities of families of complex hypersurface-germs | [
"Camille Plenat",
"David Trotman"
] | 23 Feb 2012 (<a href="https://arxiv.org/abs/1202.5177v1">v1</a>), last revised 8 Jun 2012 (this version, v5) | 6 pages 0 figure | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1202.5177 | We show that the possible drop in multiplicity in an analytic family $F(z,t)$ of complex analytic hypersurface singularities with constant Milnor number is controlled by the powers of $t$. We prove equimultiplicity of $\mu$-constant families of the form $f + tg + t^2h$ if the singular set of the tangent cone of $\{f = ... | math-31-part-2.zip/1202.5177.pdf |
1406.1073 | On the motive of some hyperKaehler varieties | [
"Charles Vial"
] | 4 Jun 2014 (<a href="https://arxiv.org/abs/1406.1073v1">v1</a>), last revised 7 Apr 2015 (this version, v2) | 9 pages. To appear in Crelle's journal | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1406.1073 | We show that the motive of the Hilbert scheme of length-$n$ subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety obtained by Shermenev, Beauville, and Deninger and Murre. | math-31-part-2.zip/1406.1073.pdf |
1910.06208 | Some combinatorial aspects of generalised Bott-Samelson varieties | [
"Michel Brion",
"S. Senthamarai Kannan"
] | 14 Oct 2019 | 22 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.1910.06208 | We obtain two combinatorial results: an equality of Weyl groups and an inequality of roots, in the setting of generalised Bott-Samelson resolutions of minuscule Schubert varieties. These results are used in the companion paper [BK19] to describe minimal rational curves on these resolutions, and their relation to lines ... | math-32-part-2.zip/1910.06208.pdf |
0707.3251 | Picard-graded Betti numbers and the defining ideals of Cox rings | [
"Antonio Laface",
"Mauricio Velasco"
] | 22 Jul 2007 | 21 pages, 3 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.0707.3251 | Let X be a smooth projective variety with torsion-free Picard group. We introduce complexes of vector spaces whose homology determines the structure of the minimal free resolution of the Cox ring of X over the polynomial ring and show how the homology of these complexes can be studied by purely geometric methods. As an... | math-30-part-2.zip/0707.3251.pdf |
2209.01481 | Decomposition of Frobenius pushforwards of line bundles on wonderful compactifications | [
"Merrick Cai",
"Vasily Krylov"
] | 3 Sep 2022 | 54 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.2209.01481 | De Concini-Procesi introduced varieties known as wonderful compactifications, which are smooth projective compactifications of semisimple adjoint groups $G$. We study the Frobenius pushforwards of invertible sheaves on the wonderful compactifications, and in particular its decomposition into locally free subsheaves. We... | math-33-part-1.zip/2209.01481.pdf |
1409.2029 | Rationality of cycles over function fields of $SL_1(A)$-torsors | [
"Raphaël Fino"
] | 6 Sep 2014 | 7 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1409.2029 | In this note we prove a result comparing rationality of algebraic cycles over the function field of a $SL_1(A)$-torsor for a central simple algebra $A$ and over the base field. | math-31-part-2.zip/1409.2029.pdf |
2212.09364 | On the GIT stability of linear systems of hypersurfaces in projective space | [
"Masafumi Hattori",
"Aline Zanardini"
] | 19 Dec 2022 (<a href="https://arxiv.org/abs/2212.09364v1">v1</a>), last revised 27 Dec 2022 (this version, v2) | 23 pages. References updated | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2212.09364 | We consider the problem of classifying linear systems of hypersurfaces (of a fixed degree) in some projective space up to projective equivalence via geometric invariant theory (GIT). We provide an explicit criterion that solves the problem completely. As an application, we consider a few relevant geometric examples rec... | math-33-part-1.zip/2212.09364.pdf |
1505.04596 | Constructing colimits by gluing vector bundles | [
"Daniel Schäppi"
] | 18 May 2015 | 63 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Category Theory (math.CT) | https://doi.org/10.48550/arXiv.1505.04596 | As already observed by Gabriel, coherent sheaves on schemes obtained by gluing affine open subsets can be described by a simple gluing construction. An example due to Ferrand shows that this fails in general for pushouts along closed immersions, though the gluing construction still works for flat coherent sheaves. <br>... | math-32-part-1.zip/1505.04596.pdf |
1510.05079 | Log canonical thresholds on group compactifications | [
"Thibaut Delcroix"
] | 17 Oct 2015 (<a href="https://arxiv.org/abs/1510.05079v1">v1</a>), last revised 16 Nov 2015 (this version, v2) | This article contains a part of the results from the author's PhD Thesis. v2: reference added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Differential Geometry (math.DG) | https://doi.org/10.48550/arXiv.1510.05079 | We compute the log canonical thresholds of non-negatively curved singular hermitian metrics on ample linearized line bundles on bi-equivariant group compactifications of complex reductive groups. To this end, we associate to any such metric a convex function whose asymptotic behavior determines the log canonical thresh... | math-32-part-1.zip/1510.05079.pdf |
2003.09203 | Tropical curves and covers and their moduli spaces | [
"Hannah Markwig"
] | 20 Mar 2020 | Comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2003.09203 | This is a survey article written for the Jahresberichte der DMV. <br>Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and covers of tropical curves maps between metric graphs satisfying certain condit... | math-32-part-2.zip/2003.09203.pdf |
math/0507074 | A remark on a theorem of M. Haiman | [
"Victor Ginzburg"
] | 4 Jul 2005 | 5pp | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.math/0507074 | We deduce a special case of a theorem of M. Haiman concerning alternating polynomials in 2n variables from our results about almost commuting variety, obtained earlier in a joint work with W.-L. Gan. | math-34-part-1.zip/math_0507074.pdf |
0812.4245 | Polars of real singular curves | [
"Heidi Camilla Mork",
"Ragni Piene"
] | 22 Dec 2008 | 18 pages, 16 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0812.4245 | Polar varieties have in recent years been used by Bank, Giusti, Heintz, Mbakop, and Pardo, and by Safey El Din and Schost, to find efficient procedures for determining points on all real components of a given non-singular algebraic variety. In this note we review the classical notion of polars and polar varieties, as w... | math-31-part-1.zip/0812.4245.pdf |
2006.03668 | Volume and symplectic structure for l-adic local systems | [
"G. Pappas"
] | 5 Jun 2020 (<a href="https://arxiv.org/abs/2006.03668v1">v1</a>), last revised 2 Jun 2021 (this version, v3) | 51 pp, final version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.2006.03668 | We introduce a notion of volume for an l-adic local system over an algebraic curve and, under some conditions, give a symplectic form on the rigid analytic deformation space of the corresponding geometric local system. These constructions can be viewed as arithmetic analogues of the volume and the Chern-Simons invarian... | math-32-part-2.zip/2006.03668.pdf |
math/0605094 | Gluing in tensor triangular geometry | [
"Paul Balmer",
"Giordano Favi"
] | 3 May 2006 (<a href="https://arxiv.org/abs/math/0605094v1">v1</a>), last revised 5 May 2006 (this version, v2) | 20 pages, added missing bibliography | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Category Theory (math.CT); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.math/0605094 | We discuss gluing of objects and gluing of morphisms in tensor triangulated categories. We illustrate the results by producing, among other things, a Mayer-Vietoris exact sequence involving Picard groups. | math-34-part-1.zip/math_0605094.pdf |
1909.00772 | Counting curves in a linear system with upto eight singular points | [
"Somnath Basu",
"Ritwik Mukherjee"
] | 2 Sep 2019 | 52 pages, 10 figures. Comments are welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1909.00772 | In this paper, we develop a systematic approach to enumerate curves with a certain number of nodes and one further singularity which maybe more degenerate. As a result, we obtain an explicit formula for the number of curves in a sufficiently ample linear system, passing through the right number of generic points, that ... | math-32-part-2.zip/1909.00772.pdf |
2211.07450 | Birational Reparametrizations of Surfaces | [
"Jorge Caravantes",
"Sonia Pérez-Díaz",
"J. Rafael Sendra"
] | 14 Nov 2022 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2211.07450 | Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational parametrization with empty base locus, and the input parametrization is transversal, the de... | math-33-part-1.zip/2211.07450.pdf | |
2209.14791 | Rational singularities for moment maps of totally negative quivers | [
"Tanguy Vernet"
] | 29 Sep 2022 (<a href="https://arxiv.org/abs/2209.14791v1">v1</a>), last revised 12 Aug 2024 (this version, v4) | Accepted version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.2209.14791 | We prove that the zero-fiber of the moment map of a totally negative quiver has rational singularities. Our proof consists in generalizing dimension bounds on jet spaces of this fiber, which were introduced by Budur. We also transfer the rational singularities property to other moduli spaces of objects in 2-Calabi-Yau ... | math-33-part-1.zip/2209.14791.pdf |
2310.08125 | A C_2-equivariant Gabber presentation lemma | [
"Tom Bachmann"
] | 12 Oct 2023 (<a href="https://arxiv.org/abs/2310.08125v1">v1</a>), last revised 7 Mar 2024 (this version, v2) | 6 pages; v2: some typos corrected, some applications added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); K-Theory and Homology (math.KT) | https://doi.org/10.48550/arXiv.2310.08125 | We establish a version of Gabber's presentation lemma in the setting of varieties with an action by the finite group of order 2. | math-33-part-2.zip/2310.08125.pdf |
2307.07543 | Ulrich sheaves, the arithmetic writhe and algebraic isotopies of space curves | [
"Daniele Agostini",
"Mario Kummer"
] | 14 Jul 2023 (<a href="https://arxiv.org/abs/2307.07543v1">v1</a>), last revised 28 Jan 2025 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.2307.07543 | We establish a connection between the theory of Ulrich sheaves and $\mathbb{A}^1$-homotopy theory. For instance, we prove that the $\mathbb{A}^1$-degree of a morphism between projective varieties, that is relatively oriented by an Ulrich sheaf, is constant on the target even when it is not $\mathbb{A}^1$-chain connecte... | math-33-part-2.zip/2307.07543.pdf | |
math/0402338 | Classification of Poisson surfaces | [
"Claudio Bartocci",
"Emanuele Macr\\`ı"
] | 20 Feb 2004 | LaTeX file, 8 pages; to be published in "Communications in Contemporary Mathematics" | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0402338 | We study complex projective surfaces admitting a Poisson structure. We prove a classification theorem and count how many independent Poisson structures there are on a given Poisson surface. | math-34-part-1.zip/math_0402338.pdf |
1205.3429 | Weierstrass equations for Jacobian fibrations on a certain K3 surface | [
"Kazuki Utsumi"
] | 15 May 2012 (<a href="https://arxiv.org/abs/1205.3429v1">v1</a>), last revised 23 Jul 2012 (this version, v3) | 46 pages, 31 figures, to appear in Hiroshima Mathematical Journal, Added the list of Weierstrass equations and modified some misprint | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1205.3429 | In this paper we give the Weierstrass equations for Jacobian fibrations on the K3 surface that is the minimal resolution of the double covering of projective plane ramified along generic six lines. | math-31-part-2.zip/1205.3429.pdf |
1012.0979 | Log del Pezzo Surfaces of Rank 2 and Cartier Index 3 with a Unique Singularity | [
"Fei Wang"
] | 5 Dec 2010 | 19 pages, 6 figures, to appear in manuscripta mathematica | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1012.0979 | Log del Pezzo surfaces play the role of the opposite of surfaces of general type. We will completely classify all the log del Pezzo surfaces of rank 2 and Cartier index 3 with a unique singularity. | math-31-part-1.zip/1012.0979.pdf |
math/0403056 | Equiramified deformations of covers in positive characteristic | [
"Rachel Pries"
] | 2 Mar 2004 (<a href="https://arxiv.org/abs/math/0403056v1">v1</a>), last revised 13 Jul 2005 (this version, v3) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.math/0403056 | Suppose $\phi$ is a wildly ramified cover of germs of curves defined over an algebraically closed field of characteristic p. We study unobstructed deformations of $\phi$ in equal characteristic, which are equiramified in that the branch locus is constant and the ramification filtration is fixed. We show that the moduli... | math-34-part-1.zip/math_0403056.pdf | |
2303.11300 | Non-degeneracy conditions for plane branches | [
"Beata Gryszka",
"Janusz Gwoździewicz"
] | 20 Mar 2023 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2303.11300 | Let $x=t^n$, $y=\sum_{i=1}^{\infty}a_it^i$ be a parametrisation of the germ of a complex plane analytic curve $\Gamma$ at the origin. Then $\Gamma$ has the implicit equation $f(x,y)=0$ in the neighbourhood of the origin, where $f=\sum c_{ij}x^iy^j$ is a Weierstrass polynomial in $\mathbb{C}[[x]][y]$ of degree $n$. Ever... | math-33-part-2.zip/2303.11300.pdf | |
0909.0817 | Equivalences and stratified flops | [
"Sabin Cautis"
] | 4 Sep 2009 (<a href="https://arxiv.org/abs/0909.0817v1">v1</a>), last revised 9 Jun 2011 (this version, v2) | 22 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0909.0817 | We construct natural equivalences between derived categories of coherent sheaves on the local models for stratified Mukai or Atiyah flops (of type A). | math-31-part-1.zip/0909.0817.pdf |
2201.01234 | On the $p$-adic theory of local models | [
"Johannes Anschütz",
"Ian Gleason",
"João Lourenço",
"Timo Richarz"
] | 4 Jan 2022 | Comments welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2201.01234 | We prove the Scholze--Weinstein conjecture on the existence and uniqueness of local models of local Shimura varieties and the test function conjecture of Haines--Kottwitz in this setting. In order to achieve this, we establish the specialization principle for well-behaved $p$-adic kimberlites, show that these include t... | math-33-part-1.zip/2201.01234.pdf |
math/0309091 | Signed quivers, symmetric quivers, and root systems | [
"D.A.Shmelkin"
] | 5 Sep 2003 | 20 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.math/0309091 | We define a special sort of weighted oriented graphs, signed quivers. Each of these yields a symmetric quiver, i.e., a quiver endowed with an involutive anti-automorphism and the inherited signs. We develop a representation theory of symmetric quivers, in particular we describe the indecomposable symmetric representati... | math-34-part-1.zip/math_0309091.pdf |
1607.07979 | Local polar varieties in the geometric study of singularities | [
"Arturo Giles Flores",
"Bernard Teissier"
] | 27 Jul 2016 (<a href="https://arxiv.org/abs/1607.07979v1">v1</a>), last revised 13 Dec 2017 (this version, v3) | In this new version, several misprints and incoherencies of notations have been corrected, and some problems have been added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1607.07979 | This text presents several aspects of the theory of equisingularity of complex analytic spaces from the standpoint of Whitney conditions. The goal is to describe from the geometrical, topological, and algebraic viewpoints a canonical locally finite partition of a reduced complex analytic space $X$ into nonsingular stra... | math-32-part-1.zip/1607.07979.pdf |
1205.6124 | Invariance of o-minimal cohomology with definably compact supports | [
"Mario J. Edmundo",
"Luca Prelli"
] | 28 May 2012 (<a href="https://arxiv.org/abs/1205.6124v1">v1</a>), last revised 13 Jul 2015 (this version, v3) | 30 pages, uses xy-pic | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1205.6124 | In this paper we find general criteria to ensure that, in an arbitrary o-minimal structure, the o-minimal cohomology without supports and with definably compact supports of a definable space with coefficients in a sheaf is invariant in elementary extensions and in o-minimal expansions. We also prove the o-minimal analo... | math-31-part-2.zip/1205.6124.pdf |
math/0609162 | Weighted Blowups and Mirror Symmetry for Toric Surfaces | [
"Gabriel D. Kerr"
] | 6 Sep 2006 | 55 pages, 14 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.math/0609162 | This paper explores homological mirror symmetry for weighted blowups of toric varieties. It will be shown that both the A-model and B-model categories have natural semiorthogonal decompositions. An explicit equivalence of the right orthogonal categories will be shown for the case of toric surfaces. | math-34-part-1.zip/math_0609162.pdf |
math/0305094 | Sur la cohomologie des systèmes locaux sur les espaces des modules des courbes de genre 2 et des surfaces abéliennes | [
"Carel Faber",
"Gerard van der Geer"
] | 6 May 2003 | 7 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.math/0305094 | We consider the cohomology of local systems on the moduli space of curves of genus 2 and the moduli space of abelian surfaces. We give an explicit formula for the Eisenstein cohomology and a conjectural formula for the endoscopic contribution. We show how counting curves over finite fields provides us with detailed inf... | math-34-part-1.zip/math_0305094.pdf |
alg-geom/9402008 | Variation of Geometric Invariant Theory Quotients | [
"Igor V. Dolgachev",
"Yi Hu"
] | 9 Feb 1994 (<a href="https://arxiv.org/abs/alg-geom/9402008v1">v1</a>), last revised 13 Dec 1995 (this version, v4) | Plain Tex, Revised version, to appear in Publ. Math. I.H.E.S | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9402008 | Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized varieties, etc.). The quotient depends on a choice of an ample linearized line bundl... | small_categories-00.zip/alg-geom_9402008.pdf |
2202.05202 | The topology of Calabi-Yau threefolds with Picard number three | [
"P.M.H. Wilson"
] | 10 Feb 2022 (<a href="https://arxiv.org/abs/2202.05202v1">v1</a>), last revised 15 May 2023 (this version, v6) | 37 pages, 6 figures. New Section 5 added on boundedness questions | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2202.05202 | We ask about the simply connected compact smooth 6-manifolds which can support structures of Calabi-Yau threefolds. In particular, we study the interesting case of Calabi-Yau threefolds $X$ with second betti number 3. We have a cup-product cubic form on the second integral cohomology, a linear form given by the second ... | math-33-part-1.zip/2202.05202.pdf |
2409.12542 | On the degree of a modular map | [
"Ciro Ciliberto",
"Alessandro verra"
] | 19 Sep 2024 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2409.12542 | Let $X$ be a general cubic hypersurface in $\mathbb P^4$. If $x\in X$ is a general point there are exactly six distinct lines in $X$ passing through $x$, that lie on the rank 3 quadric cone with vertex $x$ of lines that have intersection multiplicity at least 3 with $X$ in $x$. So there is a natural rational map $X\das... | math-33-part-2.zip/2409.12542.pdf | |
1604.05954 | An exceptional locus in the perfect compactification of $A_g$ | [
"N. Shepherd-Barron"
] | 20 Apr 2016 (<a href="https://arxiv.org/abs/1604.05954v1">v1</a>), last revised 7 Sep 2019 (this version, v2) | Unnecessary remarks about stack-theoretic Satake compactifications have been removed | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1604.05954 | The line bundle $12M-D$ on the perfect compactification $A_g^P$ is nef; we show here that in positive characteristic it is semi-ample and that in all characteristics its exceptional locus is the closure of the locus of abelian varieties with an elliptic factor. | math-32-part-1.zip/1604.05954.pdf |
2403.09934 | Symmetric products of Galois-Maximal varieties | [
"Javier Orts"
] | 15 Mar 2024 (<a href="https://arxiv.org/abs/2403.09934v1">v1</a>), last revised 8 Sep 2024 (this version, v2) | 16 pages, 1 figure | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.2403.09934 | The main result of this paper is the proof that all the symmetric products of a (finite) Galois-Maximal space are also Galois-Maximal spaces. This applies to the special case of real algebraic varieties, solving the problem first stated by Biswas and D'Mello in \cite{biswas&d'mello:symmetric_products_M-curv... | math-33-part-2.zip/2403.09934.pdf |
math/0108222 | Belyi's theorem revisited | [
"Bernhard Köck"
] | 31 Aug 2001 (<a href="https://arxiv.org/abs/math/0108222v1">v1</a>), last revised 27 Apr 2014 (this version, v2) | 12 pages; v2: minor changes | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.math/0108222 | We give an elementary, self-contained and quick proof of Belyi's theorem. As a by-product of our proof we obtain an explicit bound for the degree of the defining number field of a Belyi surface. | math-34-part-1.zip/math_0108222.pdf |
alg-geom/9701018 | Exemples de composantes irréductibles et non réduites du schéma de Hilbert des courbes lisses et connexes de ${\bf P}^3$ (II) | [
"Said Azziz"
] | 29 Jan 1997 | 28 pages, in French Plain-Tex | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9701018 | Soit $H_{d,g}$ le schéma de Hilbert des courbes lisses et connexes de degré $d$ et genre $g$ de l'espace projectif ${\bf P}^3$ sur un corps $k$ algébriquement clos de caractéristique nulle. Le but principal de cet article est d'exhiber des composantes irréductibles et non réduites de $H_{d,g}$ dont l'élémen... | small_categories-00.zip/alg-geom_9701018.pdf |
2302.02736 | Narasimhan--Ramanan branes and wobbly Higgs bundles | [
"Emilio Franco",
"Peter B. Gothen",
"André G. Oliveira",
"Ana Peón-Nieto"
] | 6 Feb 2023 (<a href="https://arxiv.org/abs/2302.02736v1">v1</a>), last revised 20 Oct 2023 (this version, v2) | 20 pages, minor corrections | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2302.02736 | Narasimhan--Ramanan branes were introduced by the authors in a previous article. They consist of a family of $BBB$-branes inside the moduli space of Higgs bundles, and a family of complex Lagrangian subvarieties. It was conjectured that these complex Lagrangian subvarieties support the $BAA$-branes that are mirror dual... | math-33-part-1.zip/2302.02736.pdf |
2011.14938 | A triangulation of semi-algebraic sets concerning an analytical condition for shortest-length curves | [
"Chengcheng Yang"
] | 30 Nov 2020 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Classical Analysis and ODEs (math.CA) | https://doi.org/10.48550/arXiv.2011.14938 | This paper concerns an analytical stratification question of real algebraic and semi-algebraic sets. For Whitney's stratification in 1957, it partitions a real algebraic set into partial algebraic manifolds\cite{W}. In 1975 Hironaka reproved that a real algebraic set is triangulable and also generalized it to semi-... | math-33-part-1.zip/2011.14938.pdf | |
2307.03745 | Frobenius on the cohomology of thickenings | [
"Bhargav Bhatt",
"Manuel Blickle",
"Gennady Lyubeznik",
"Anurag K. Singh",
"Wenliang Zhang"
] | 7 Jul 2023 | Comments welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.2307.03745 | We investigate the injectivity of the Frobenius map on thickenings of smooth varieties in projective space over a field of positive characteristic. We obtain uniform bounds -- i.e., independent of the characteristic -- on the thickening that ensures an injective Frobenius map when the projective variety is a smooth com... | math-33-part-2.zip/2307.03745.pdf |
2406.06205 | Rooted trees with level structures, $Ω$-classes and double ramification cycles | [
"Xavier Blot",
"Danilo Lewański",
"Sergey Shadrin"
] | 10 Jun 2024 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2406.06205 | We prove a new system of relations in the tautological ring of the moduli space of curves involving stable rooted trees with level structure decorated by the top Chern class of the Hodge bundle and $\Omega$-classes and double ramification structures. In particular, this resolves a recent conjecture on these relations a... | math-33-part-2.zip/2406.06205.pdf | |
2305.06128 | Double covers of curves on Nikulin surfaces | [
"Simona D'Evangelista",
"Margherita Lelli-Chiesa"
] | 10 May 2023 | 16 pages, to appear in the AMS Contemporary Mathematics volume in honor of Peter Newstead | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2305.06128 | We survey basic results concerning Prym varieties, the Prym-Brill-Noether theory initiated by Welters, and Brill-Noether theory of general étale double covers of curves of genus g>=2. We then specialize to curves on Nikulin surfaces and show that étale double covers of curves on Nikulin surfaces of standard type do ... | math-33-part-2.zip/2305.06128.pdf |
math/0502461 | Factorization Theorem for Projective Varieties with Finite Quotient Singularities | [
"Yi Hu"
] | 22 Feb 2005 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Differential Geometry (math.DG) | https://doi.org/10.48550/arXiv.math/0502461 | In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying the theory of Variation of Geometric Invariant Theory Quotients ([3]), we show tha... | math-34-part-1.zip/math_0502461.pdf | |
2508.04135 | Lagrangian Fibrations onto Varieties with Isolated Quotient Singularities | [
"Niklas Müller",
"Zheng Xu"
] | 6 Aug 2025 | 12 pages. Comments are welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2508.04135 | In this note, we show that if $f\colon M\rightarrow X$ is a germ of a projective Lagrangian fibration from a holomorphic symplectic manifold $M$ onto a normal analytic variety $X$ with isolated quotient singularities, then $X$ is smooth. In particular, if $f\colon M\rightarrow X$ is a Lagrangian fibration from a hyper-... | math-34-part-1.zip/2508.04135.pdf |
alg-geom/9411002 | The minimal number of singular fibers of a semistable curves over P^1 | [
"Sheng-Li Tan"
] | 8 Nov 1994 | 6 pages, AmSTeX | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9411002 | In this paper, we shall prove Beauville's conjecture: if $f:S \to P^1$ is a non-trivial semistable fibration of genus g>1, then $f$ admits at least 5 singular fibers. We have also constructed an example of genus 2 with 5 singular fibers. This paper will appear in the Journal of Algebraic Geometry. | small_categories-00.zip/alg-geom_9411002.pdf |
2011.07452 | Local topological obstruction for divisors | [
"Indranil Biswas",
"Ananyo Dan"
] | 15 Nov 2020 | To appear in Revista Matemática Complutense | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2011.07452 | Given a smooth, projective variety $X$ and an effective divisor $D\,\subseteq\, X$, it is well-known that the (topological) obstruction to the deformation of the fundamental class of $D$ as a Hodge class, lies in $H^2(\mathcal{O}_X)$. In this article, we replace $H^2(\mathcal{O}_X)$ by $H^2_D(\mathcal{O}_X)$ and give a... | math-33-part-1.zip/2011.07452.pdf |
1406.1451 | Symmetry Detection of Rational Space Curves from their Curvature and Torsion | [
"Juan Gerardo Alcázar",
"Carlos Hermoso",
"Georg Muntingh"
] | 5 Jun 2014 (<a href="https://arxiv.org/abs/1406.1451v1">v1</a>), last revised 25 Jan 2015 (this version, v2) | 25 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1406.1451 | We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method is significantly faster, simpler, and more general than an earlier method addressing a similar pr... | math-31-part-2.zip/1406.1451.pdf |
2507.17642 | Motivic classes of fixed-generators Hilbert schemes of unibranch curve singularities and Igusa zeta functions | [
"Ilaria Rossinelli"
] | 23 Jul 2025 (<a href="https://arxiv.org/abs/2507.17642v1">v1</a>), last revised 24 Jul 2025 (this version, v2) | 24 pages, comments welcome! Minor corrections, results unchanged | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2507.17642 | This paper delves into the study of Hilbert schemes of unibranch plane curves whose points have a fixed number of minimal generators. Building on the work of Oblomkov, Rasmussen and Shende we provide a formula for their motivic classes and investigate the relationship with principal Hilbert schemes of the same given un... | math-34-part-1.zip/2507.17642.pdf |
1903.10240 | On vector bundles over reducible curves with a node | [
"Sonia Brivio",
"Filippo F. Favale"
] | 25 Mar 2019 (<a href="https://arxiv.org/abs/1903.10240v1">v1</a>), last revised 28 Jul 2020 (this version, v2) | 17 pages, 1 figure. Final version published on "Advances in Geometry" | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1903.10240 | Let $C$ be a curve with two smooth components and a single node. Let $\mathcal{U}_C(r,w,\chi)$ be the moduli space of $w$-semistable classes of depth one sheaves on $C$ having rank $r$ on both components and Euler characteristic $\chi$. In this paper, under suitable assumptions, we produce a projective bundle over the ... | math-32-part-2.zip/1903.10240.pdf |
2507.00200 | Linkage of sheaves of modules | [
"Farhad Rahmati",
"Khadijeh Sayyari"
] | 30 Jun 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.2507.00200 | Inspired by the works in linkage theory of modules, we define the concept of linkage of sheaves of modules as a generalization of linkage of modules. Thus, we expressed it in geometry algebraic language. We show that the linkedness of sheaves is a locally property. As an important result, we have shown that the sheaf o... | math-34-part-1.zip/2507.00200.pdf | |
0809.1233 | The ring of projective invariants of eight points on the line via representation theory | [
"Ben Howard",
"John Millson",
"Andrew Snowden",
"Ravi Vakil"
] | 7 Sep 2008 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0809.1233 | The ring of projective invariants of eight ordered points on the line is a quotient of the polynomial ring on V, where V is a fourteen-dimensional representation of S_8, by an ideal I_8, so the modular fivefold (P^1)^8 // GL(2) is Proj(Sym* (V)/I_8). We show that there is a unique cubic hypersurface S in PV whose equat... | math-31-part-1.zip/0809.1233.pdf | |
math/0108108 | The Toda conjecture | [
"Ezra Getzler"
] | 15 Aug 2001 | Proceedings of conference on symplectic geometry, KIAS, Seoul, August 2000 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.math/0108108 | We study the Toda conjecture of Eguchi and Yang for the Gromov-Witten invariants of CP^1,using the bihamiltonian method of the formal calculus of variations. We also study its relationship to the Virasoro conjecture for CP^1, recently proved by Givental (<a href="https://arxiv.org/abs/math.AG/0108100" data-arxiv-id="ma... | math-34-part-1.zip/math_0108108.pdf |
1912.01689 | Comparing the Kirwan and noncommutative resolutions of quotient varieties | [
"Špela Špenko",
"Michel Van den Bergh"
] | 3 Dec 2019 | 40 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Rings and Algebras (math.RA); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1912.01689 | Let a reductive group $G$ act on a smooth variety $X$ such that a good quotient $X{/\!\!/}G$ exists. We show that the derived category of a noncommutative crepant resolution (NCCR) of $X{/\!\!/} G$, obtained from a $G$-equivariant vector bundle on $X$, can be embedded in the derived category of the (canonical, stacky) ... | math-32-part-2.zip/1912.01689.pdf |
2405.16338 | Projective hypersurfaces in tropical scheme theory I: the Macaulay ideal | [
"Alex Fink",
"Jeffrey Giansiracusa",
"Noah Giansiracusa",
"Joshua Mundinger"
] | 25 May 2024 | Appendix by Joshua Mundinger. 21pp | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.2405.16338 | A "tropical ideal" is an ideal in the idempotent semiring of tropical polynomials that is also, degree by degree, a tropical linear space. We introduce a construction based on transversal matroids that canonically extends any principal ideal to a tropical ideal. We call this the Macaulay tropical ideal. It has ... | math-33-part-2.zip/2405.16338.pdf |
1105.4853 | Notes characterising higher and derived stacks concretely | [
"J.P.Pridham"
] | 24 May 2011 (<a href="https://arxiv.org/abs/1105.4853v1">v1</a>), last revised 25 Jun 2024 (this version, v4) | Only 11 pages long; v2 slightly expanded and typos fixed; v3 refs updated, Theorems 3.3, 5.11 and 5.17 added; v4 corrected typo in Definition 5.10 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.1105.4853 | This is an informal summary of the main concepts in <a href="https://arxiv.org/abs/0905.4044" data-arxiv-id="0905.4044" class="link-https">arXiv:0905.4044</a>, based on notes of various seminars. It gives constructions of higher and derived stacks without recourse to the extensive theory developed by Toen, Vezzosi and ... | math-31-part-1.zip/1105.4853.pdf |
1804.09797 | On the locus of curves with an odd subcanonical marked point | [
"Andre Contiero",
"Aislan Leal Fontes"
] | 25 Apr 2018 | 20 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1804.09797 | We present an explicit construction of a compactification of the locus of smooth curves whose symmetric Weierstrass semigroup at a marked point is odd. The construction is an extension of Stoehr's techniques using Pinkham'sequivariant deformation of monomial curves by exploring syzygies. As an application we pr... | math-32-part-2.zip/1804.09797.pdf |
0907.2338 | A view on extending morphisms from ample divisors | [
"Mauro C. Beltrametti",
"Paltin Ionescu"
] | 14 Jul 2009 | To Appear in: Interactions of Classical and Numerical Algebraic Geometry, ed. by A. Bates, G. Besana and S. Di Rocco, Contemporary Mathematics, American Mathematical Society | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0907.2338 | The philosophy that ``a projective manifold is more special than any of its smooth hyperplane sections" was one of the classical principles of projective geometry. Lefschetz type results and related vanishing theorems were among the typically used techniques. We shall survey most of the problems, results and conjec... | math-31-part-1.zip/0907.2338.pdf |
0811.2781 | A Giambelli formula for isotropic Grassmannians | [
"Anders S. Buch",
"Andrew Kresch",
"Harry Tamvakis"
] | 17 Nov 2008 (<a href="https://arxiv.org/abs/0811.2781v1">v1</a>), last revised 4 Aug 2010 (this version, v2) | 39 pages; improvements and corrections made to the exposition | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0811.2781 | Let X be a symplectic or odd orthogonal Grassmannian parametrizing isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in H^*(X,Z) as a polynomial in certain special Schubert classes. We study theta polynomia... | math-31-part-1.zip/0811.2781.pdf |
1308.6454 | Resultants and the Borcherds Phi-function | [
"Shu Kawaguchi",
"Shigeru Mukai",
"Ken-Ichi Yoshikawa"
] | 29 Aug 2013 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1308.6454 | The Borcherds Phi-function is the automorphic form on the moduli space of Enriques surfaces characterizing the discriminant locus. In this paper, we give an algebro-geometric construction of the Borcherds Phi-function. | math-31-part-2.zip/1308.6454.pdf |
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