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 |
|---|---|---|---|---|---|---|---|---|---|
math/0404516 | Restricting linear syzygies: algebra and geometry | [
"David Eisenbud",
"Mark Green",
"Klaus Hulek",
"Sorin Popescu"
] | 28 Apr 2004 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.math/0404516 | In this paper we derive geometric consequences from the presence of a long strand of linear syzygies in the minimal free resolution of a closed scheme in projective space whose homogeneous ideal is generated by quadrics. These consequences are given in terms of intersections with arbitrary linear subspaces. We use our ... | math-34-part-1.zip/math_0404516.pdf | |
alg-geom/9709007 | The enumerative geometry of rational and elliptic curves in projective space | [
"Ravi Vakil"
] | 5 Sep 1997 | LaTeX2e, 95 pages with 18 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9709007 | We study the geometry of varieties parametrizing degree d rational and elliptic curves in P^n intersecting fixed general linear spaces and tangent to a fixed hyperplane H with fixed multiplicities along fixed general linear subspaces of H. As an application, we derive recursive formulas for the number of such curves wh... | small_categories-00.zip/alg-geom_9709007.pdf |
2412.20797 | Cohomology of flag supervarieties and resolutions of determinantal ideals. II | [
"Steven V Sam",
"Andrew Snowden"
] | 30 Dec 2024 | 29 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.2412.20797 | We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic or orthogonal group together with a semisimple representation of the periplecti... | math-33-part-2.zip/2412.20797.pdf |
1204.5448 | Compactified Jacobians and q,t-Catalan numbers, II | [
"Evgeny Gorsky",
"Mikhail Mazin"
] | 24 Apr 2012 (<a href="https://arxiv.org/abs/1204.5448v1">v1</a>), last revised 7 Dec 2013 (this version, v2) | 24 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.1204.5448 | We continue the study of the rational-slope generalized $q,t$-Catalan numbers $c_{m,n}(q,t)$. We describe generalizations of the bijective constructions of J. Haglund and N. Loehr and use them to prove a weak symmetry property $c_{m,n}(q,1)=c_{m,n}(1,q)$ for $m=kn\pm 1$. We give a bijective proof of the full symmetry $... | math-31-part-2.zip/1204.5448.pdf |
math/0012082 | Ample families, multihomogeneous spectra, and algebraization of formal schemes | [
"Holger Brenner",
"Stefan Schroeer"
] | 11 Dec 2000 (<a href="https://arxiv.org/abs/math/0012082v1">v1</a>), last revised 21 May 2007 (this version, v3) | 18 pages. Proof of Proposition 2.5 corrected and related examples included (the irrelevant ideal does not necessarily commute with base change, but its radical does) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0012082 | Generalizing homogeneous spectra for rings graded by natural numbers, we introduce multihomogeneous spectra for rings graded by abelian groups. Such homogeneous spectra have the same completeness properties as their classical counterparts, but are possibly nonseparated. We relate them to ample families of invertible sh... | math-34-part-1.zip/math_0012082.pdf |
1708.08129 | The combinatorics of Lehn's conjecture | [
"Alina Marian",
"Dragos Oprea",
"Rahul Pandharipande"
] | 27 Aug 2017 (<a href="https://arxiv.org/abs/1708.08129v1">v1</a>), last revised 12 Apr 2018 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1708.08129 | Let S be a smooth projective surface equipped with a line bundle H. Lehn's conjecture is a formula for the top Segre class of the tautological bundle associated to H on the Hilbert scheme of points of S. Voisin has recently reduced Lehn's conjecture to the vanishing of certain coefficients of special power seri... | math-32-part-1.zip/1708.08129.pdf | |
1506.00420 | Revêtements cycliques qui ne sont pas stablement rationnels | [
"Jean-Louis Colliot-Thélène",
"Alena Pirutka"
] | 1 Jun 2015 (<a href="https://arxiv.org/abs/1506.00420v1">v1</a>), last revised 1 Dec 2015 (this version, v3) | 17 pages, minor changes in Russian version, to appear in Izvestiya RAN, Ser. Math | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1506.00420 | En appliquant des méthodes développées par Kollár, Voisin, nous-mêmes, Totaro, nous montrons qu'un revêtement cyclique de $\mathbb P_{\mathbb C}^n, n\geq 3$ de degré premier $p$, ramifié le long d'une hypersurface très générale de degré $mp$ n'est pas stablement rationnel si $m(p-1) <n+1\leq mp$. En bass... | math-32-part-1.zip/1506.00420.pdf |
1711.04732 | Geometry of the Sasakura bundle | [
"Cristian Anghel"
] | 13 Nov 2017 | 12 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1711.04732 | The Sasakura bundle is a relatively recent appearance in the world of remarkable vector bundles on projective spaces. In fact, it is connected with some surfaces in $\mathbb P^4$ which missed in early classification papers. The aim of this note is to present various, scattered in the literature, aspects concerning the ... | math-32-part-1.zip/1711.04732.pdf |
math/0406536 | Classification of log del Pezzo surfaces of index $\le 2$ | [
"Valery Alexeev",
"Viacheslav V. Nikulin"
] | 25 Jun 2004 (<a href="https://arxiv.org/abs/math/0406536v1">v1</a>), last revised 10 Jun 2006 (this version, v6) | 142 pages, many figures. An expanded and improved version of this manuscript was published in Memoirs of the Mathematical Society of Japan, vol. 15 (2006) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.math/0406536 | This is an expanded version of our work [AN88], 1988, in Russian. <br>We classify del Pezzo surfaces over C with log terminal singularities of index \le 2. By classification, we understand a description of the intersection graph of all exceptional curves on an appropriate (somewhat stronger than minimal) resolution of ... | math-34-part-1.zip/math_0406536.pdf |
1110.2410 | Some subgroups of the Cremona groups | [
"Vladimir L. Popov"
] | 11 Oct 2011 (<a href="https://arxiv.org/abs/1110.2410v1">v1</a>), last revised 16 Jul 2012 (this version, v4) | The inequality $n\geqslant 6$ in Theorem 5 and Corollaries 5, 6, and 11 is replaced by $n\geqslant 5$. This gives stronger statements. In particular, it is proved the existence of (n-3)-dimensional maximal tori in the Cremona groups of rank n for every n>4 (in the previous version this was done for n>5) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Group Theory (math.GR) | https://doi.org/10.48550/arXiv.1110.2410 | We explore algebraic subgroups of of the Cremona group $\mathcal C_n$ over an algebraically closed field of characteristic zero. First, we consider some class of algebraic subgroups of $\mathcal C_n$ that we call flattenable. It contains all tori. Linearizability of the natural rational actions of flattenable subgroups... | math-31-part-1.zip/1110.2410.pdf |
2307.04395 | Higher Bernstein Polynomials and Multiple Poles of $\frac{1}{Γ(λ)} \int_X \vert f \vert^{2λ} \bar f^{-h}ρω\wedge \bar ω'$ | [
"Daniel Barlet"
] | 10 Jul 2023 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.2307.04395 | The goal of this paper is to give a converse to the main result of my previous paper \cite{[B.22]}, so to prove the existence of a pole with an hypothesis on the Bernstein polynomial of the $(a,b)$-module generated by the germ $\omega \in \Omega^{n+1}_0$. A difficulty to prove such a result comes from the use of the fo... | math-33-part-2.zip/2307.04395.pdf | |
2501.17353 | Non-smooth regular curves via a descent approach | [
"Giuseppe Borelli",
"Camilo David Dorado Moreira",
"Rodrigo Salomão"
] | 29 Jan 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2501.17353 | This paper aims to continue the classification of non-smooth regular curves, but over fields of characteristic three. These curves were originally introduced by Zariski as generic fibers of counterexamples to Bertini's theorem on the variation of singular points of linear series. Such a classification has been intr... | math-33-part-2.zip/2501.17353.pdf | |
2411.17268 | Extension of adapted differentials on klt orbifolds | [
"Pedro Núñez"
] | 26 Nov 2024 | 16 pages, all comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2411.17268 | Given a geometric orbifold $(X,\Delta)$ in the sense of Campana, adapted reflexive differentials with respect to this orbifold are defined on suitably ramified covers of $X$. We show that if the orbifold $(X,\Delta)$ is klt, then any such reflexive differential form can be extended to a regular differential form on a r... | math-33-part-2.zip/2411.17268.pdf |
math/9906209 | Curves in the double plane | [
"Robin Hartshorne",
"Enrico Schlesinger"
] | 30 Jun 1999 | 20 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/9906209 | We study locally Cohen-Macaulay curves in projective three-space which are contained in a double plane 2H, thus completing the classification of curves lying on surfaces of degree two. We describe the irreducible components of the Hilbert schemes of locally Cohen-Macaulay curves in 2H of given degree and arithmetic gen... | math-34-part-2.zip/math_9906209.pdf |
1304.0653 | Ulrich Bundles on Quartic Surfaces with Picard Number 1 | [
"Emre Coskun"
] | 2 Apr 2013 | Final version. To appear in Comptes Rendus Mathematique | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1304.0653 | In this note, we prove that there exist stable Ulrich bundles of every even rank on a smooth quartic surface $X \subset \mathbb{P}^3$ with Picard number 1. | math-31-part-2.zip/1304.0653.pdf |
1707.03845 | Limit linear series and the Amini-Baker construction | [
"Brian Osserman"
] | 12 Jul 2017 | 32 pages, 3 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1707.03845 | We draw comparisons between the author's recent construction of limit linear series for curves not of compact type and the Amini-Baker theory of limit linear series on metrized complexes, as well as the related theories of divisors on discrete graphs and on metric graphs. From these we conclude that the author'... | math-32-part-1.zip/1707.03845.pdf |
1108.3733 | Syzygy algebras for the Segre embeddings | [
"Igor V. Netay"
] | 18 Aug 2011 (<a href="https://arxiv.org/abs/1108.3733v1">v1</a>), last revised 13 Jun 2013 (this version, v2) | 17 pages, 11 pictures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.1108.3733 | We describe the syzygy spaces for the Segre embedding $\mathbb{P}(U)\times\mathbb{P}(V)\subset\mathbb{P}(U\otimes V)$ in terms of representations of ${\rm GL}(U)\times {\rm GL}(V)$ and construct the minimal resolutions of the sheaves $\mathscr{O}_{\mathbb{P}(U)\times\mathbb{P}(V)}(a,b)$ in $D(\mathbb{P}(U\otimes V))$ f... | math-31-part-1.zip/1108.3733.pdf |
1408.5358 | Cox rings over nonclosed fields | [
"Ulrich Derenthal",
"Marta Pieropan"
] | 22 Aug 2014 (<a href="https://arxiv.org/abs/1408.5358v1">v1</a>), last revised 4 Sep 2018 (this version, v3) | 30 pages; reorganized, Section 5 shortened | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1408.5358 | We give a definition of Cox rings and Cox sheaves for varieties over nonclosed fields that is compatible with torsors under quasitori, including universal torsors. We study their existence and classification, we make the relation to torsors precise, and we present arithmetic applications. | math-31-part-2.zip/1408.5358.pdf |
2111.09134 | Degree of logarithmic foliations of type (1,1,1) | [
"Mariano Chehebar"
] | 17 Nov 2021 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV); Dynamical Systems (math.DS) | https://doi.org/10.48550/arXiv.2111.09134 | The space of codimension one holomorphic foliations of degree 1 in a projective space has an irreducible component whose general element is a logarithmic differential 1-form with simple poles in three hyperplanes. We compute its projective degree by resolving its rational parametrization map through succesive blow-ups ... | math-33-part-1.zip/2111.09134.pdf | |
2503.10564 | Tight approximation for rationally simply connected varieties | [
"Olivier Benoist",
"Olivier Wittenberg"
] | 13 Mar 2025 (<a href="https://arxiv.org/abs/2503.10564v1">v1</a>), last revised 21 Aug 2025 (this version, v3) | 18 pages; v2: minor corrections; v3: adapted numbering to conform with published version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.2503.10564 | We prove that holomorphic maps from an open subset of a complex smooth projective curve to a complex smooth projective rationally simply connected variety can be approximated by algebraic maps for the compact-open topology. This theorem can be applied in particular when the target is a smooth hypersurface of degree d i... | math-33-part-2.zip/2503.10564.pdf |
math/0510633 | Canonical heights for random iterations in certain varieties | [
"Shu Kawaguchi"
] | 28 Oct 2005 | 27 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.math/0510633 | We show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications. | math-34-part-1.zip/math_0510633.pdf |
1207.1600 | Invariants of plane curve singularities and Newton diagrams | [
"Pierrette Cassou-Noguès",
"Arkadiusz Płoski"
] | 6 Jul 2012 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1207.1600 | We present an intersection-theoretical approach to the invariants of plane curve singularities $\mu$, $\delta$, $r$ related by the Milnor formula $2\delta=\mu+r-1$. Using Newton transformations we give formulae for $\mu$, $\delta$, $r$ which imply planar versions of well-known theorems on nondegenerate singularities. | math-31-part-2.zip/1207.1600.pdf | |
math/0305328 | Jacobians with group actions and rational idempotents | [
"Angel Carocca",
"Rubi E. Rodriguez"
] | 23 May 2003 | 21 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0305328 | The object of this paper is to prove some general results about rational idempotents for a finite group $G$ and deduce from them geometric information about the components that appear in the decomposition of the Jacobian variety of a curve with $G-$action. <br>We give an algorithm to find explicit primitive rational id... | math-34-part-1.zip/math_0305328.pdf |
1009.2853 | Anticanonical divisors and curve classes on Fano manifolds | [
"Andreas Höring",
"Claire Voisin"
] | 15 Sep 2010 (<a href="https://arxiv.org/abs/1009.2853v1">v1</a>), last revised 4 Dec 2017 (this version, v2) | 17 pages, changed metadata | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1009.2853 | It is well known that the Hodge conjecture with rational coefficients holds for degree 2n-2 classes on complex projective n-folds. In this paper we study the more precise question if on a rationally connected complex projective n-fold the integral Hodge classes of degree 2n-2 are generated over $\mathbb Z$ by classes o... | math-31-part-1.zip/1009.2853.pdf |
2501.15251 | Stability conditions on the canonical line bundle of $\mathbb{P}^3$ | [
"Tianle Mao"
] | 25 Jan 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2501.15251 | We study the space of stability conditions on the total space of the canonical line bundle over the three dimensional projective space. We construct a family of geometric stability conditions and some subset of the boudary of them, which are algebraic. We also use spherical twists to construct some other stability cond... | math-33-part-2.zip/2501.15251.pdf | |
math/0003230 | Characterizations of ${\mathbb P}^n$ in arbitrary characteristic | [
"Yasuyuki Kachi",
"János Kollár"
] | 31 Mar 2000 | 10 pages, LaTeX | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0003230 | We prove that a smooth projective variety of dimension n is isomorphic to projective n-space iff the canonical class is -(n+1)-times an ample divisor. In characteristic zero this was proved by Kobayashi-Ochiai. We also extend the second adjunction theorem of Ionescu and Fujita to arbitrary characteristic. | math-34-part-1.zip/math_0003230.pdf |
0909.2013 | Crepant resolutions and brane tilings II: Tilting bundles | [
"Martin Bender",
"Sergey Mozgovoy"
] | 10 Sep 2009 | 15 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.0909.2013 | Given a brane tiling, that is, a bipartite graph on a torus, we can associate with it a singular 3-Calabi-Yau variety. Using the brane tiling, we can also construct all crepant resolutions of the above variety. We give an explicit toric description of tilting bundles on these crepant resolutions. This result proves the... | math-31-part-1.zip/0909.2013.pdf |
2306.03296 | On the proalgebraic fundamental group of topological spaces and amalgamated products of affine group schemes | [
"Christopher Deninger",
"Michael Wibmer"
] | 5 Jun 2023 | 41 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2306.03296 | The proalgebraic fundamental group of a connected topological space $X$, recently introduced by the first author, is an affine group scheme whose representations classify local systems of finite-dimensional vector spaces on $X$. In this article, we further develop the theory of the proalgebraic fundamental group, in pa... | math-33-part-2.zip/2306.03296.pdf |
1309.5704 | A primitive change of variables formula for schemic motivic integration | [
"Andrew R. Stout"
] | 23 Sep 2013 | 10 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1309.5704 | We develop further the theory of integrable functions within the theory of relative simplicial motivic measures. We provide a primitive change of variables formula for this theory. | math-31-part-2.zip/1309.5704.pdf |
alg-geom/9305002 | A Finiteness Theorem for Elliptic Calabi-Yau Threefolds | [
"M. Gross"
] | 3 May 1993 | 29 pages, plain TeX | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9305002 | We prove that up to birational equivalence, there exists only a finite number of families of Calabi-Yau threefolds (i.e. a threefold with trivial canonical class and factorial terminal singularities) which have an elliptic fibration to a rational surface. This strengthens a result of B. Hunt that there are only a finit... | small_categories-00.zip/alg-geom_9305002.pdf |
2203.09651 | Local-global principles for hermitian spaces over semi-global fields | [
"Jayanth Guhan"
] | 17 Mar 2022 (<a href="https://arxiv.org/abs/2203.09651v1">v1</a>), last revised 12 Apr 2022 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Number Theory (math.NT); Rings and Algebras (math.RA) | https://doi.org/10.48550/arXiv.2203.09651 | Let $K$ be a complete discrete valued field with residue field $k$ and $F$ the function field of a curve over $K$. Let $A \in {}_2Br(F)$ be a central simple algebra with an involution $\sigma$ of any kind and $F_0 =F^{\sigma}$. Let $h$ be an hermitian space over $(A, \sigma)$ and $G = SU(A, \sigma, h)$ if $\sigma$ is o... | math-33-part-1.zip/2203.09651.pdf | |
1308.3284 | Experimentation in the Schubert Calculus | [
"Abraham Martin del Campo",
"Frank Sottile"
] | 15 Aug 2013 | 30 pages. Based on Sottile's talks at 2012 MSJ-SI on Schubert Calculus | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1308.3284 | Many aspects of Schubert calculus are easily modeled on a computer. This enables large-scale experimentation to investigate subtle and ill-understood phenomena in the Schubert calculus. A well-known web of conjectures and results in the real Schubert calculus has been inspired by this continuing experimentation. A simi... | math-31-part-2.zip/1308.3284.pdf |
alg-geom/9403006 | Hyperkaehler Embeddings II | [
"Misha Verbitsky"
] | 6 Mar 1994 | 14 pp, LaTeX 2.09 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9403006 | In the first part, Hyperkaehler Embeddings and Holomorphic symplectic Geometry I, we prove the following. Let $N$ be a closed analytic subvariety of a generic deformation of a holomorphically symplectic compact manifold $M$. Then the restriction of a holomorphic symplectic form is non-degenerate on $N$. In particular, ... | small_categories-00.zip/alg-geom_9403006.pdf |
2411.15774 | A remark on a theorem of Narasimhan and Ramanan | [
"Jagadish Pine"
] | 24 Nov 2024 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2411.15774 | In this short note, we provide an alternative proof of a notable theorem by Narasimhan and Ramanan. The theorem states that the moduli space of $S$-equivalence classes of semistable rank $2$ vector bundles over a curve $X$ of genus $2$ with trivial determinant is isomorphic to $\mathbb{P}^3$. Our proof relies on a crit... | math-33-part-2.zip/2411.15774.pdf | |
2009.07807 | Explicit coverings of families of elliptic surfaces by squares of curves | [
"Colin Ingalls",
"Adam Logan",
"Owen Patashnick"
] | 16 Sep 2020 (<a href="https://arxiv.org/abs/2009.07807v1">v1</a>), last revised 1 Dec 2021 (this version, v3) | 50 pages, 5 figures. Significant changes in response to referee's report | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2009.07807 | We show that, for each $n>0$, there is a family of elliptic surfaces which are covered by the square of a curve of genus $2n+1$, and whose Hodge structures have an action by ${\mathbb Q}(\sqrt{-n})$. By considering the case $n=3$, we show that one particular family of K3 surfaces are covered by the square of genus $... | math-33-part-1.zip/2009.07807.pdf |
0803.3444 | The Equations of Singular Loci of Ample Divisors on (Subvarieties of) Abelian Varieties | [
"Luigi Lombardi",
"Francesco Malaspina"
] | 24 Mar 2008 (<a href="https://arxiv.org/abs/0803.3444v1">v1</a>), last revised 28 Mar 2008 (this version, v2) | 9 pages, no figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0803.3444 | In this paper we consider ideal sheaves associated to the singular loci of a divisor in a linear system $|L|$ of an ample line bundle on a complex abelian variety. We prove an effective result on their (continuous) global generation, after suitable twists by powers of $L$. Moreover we show that similar results hold for... | math-31-part-1.zip/0803.3444.pdf |
math/0512079 | General sheaves over weighted projective lines | [
"William Crawley-Boevey"
] | 4 Dec 2005 (<a href="https://arxiv.org/abs/math/0512079v1">v1</a>), last revised 24 Sep 2007 (this version, v2) | 26 pages; one reference added and a change of notation | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0512079 | We develop a theory of general sheaves over weighted projective lines. We define and study a canonical decomposition, analogous to Kac's canonical decomposition for representations of quivers, study subsheaves of a general sheaf, general ranks of morphisms, and prove analogues of Schofield's results on general ... | math-34-part-1.zip/math_0512079.pdf |
math/0505679 | Approximation diophantienne dans les corps de series en plusieurs variables | [
"Guillaume Rond"
] | 31 May 2005 (<a href="https://arxiv.org/abs/math/0505679v1">v1</a>), last revised 23 Sep 2005 (this version, v2) | to appear in Annales de l'Institut Fourier, few changes following referee's comments | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.math/0505679 | We give here a result of diophantine approximation between $Ø_N$, the ring of power series in several variables, and the completion of the valuation ring that dominates $Ø_N$ for the $\m$-adic topology. We deduce from this that the Artin function of a homogenous polynomial in two variables is bounded by an affine funct... | math-34-part-1.zip/math_0505679.pdf |
1804.05297 | The $p$-adic Gelfand-Kapranov-Zelevinsky hypergeometric complex | [
"Lei Fu",
"Peigen Li",
"Daqing Wan",
"Hao Zhang"
] | 15 Apr 2018 (<a href="https://arxiv.org/abs/1804.05297v1">v1</a>), last revised 10 Oct 2022 (this version, v3) | Final version. To appear in Mathematische Annalen | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1804.05297 | To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, which are now called the GKZ hypergeometric system. Its solutions are GKZ hypergeometric functions. We study the $p$-adic counterpart of the GKZ hypergeometric system. The $p$-adic GKZ hypergeomet... | math-32-part-2.zip/1804.05297.pdf |
1103.0906 | Duality of Gauss-Manin systems associated to linear free divisors | [
"Christian Sevenheck"
] | 4 Mar 2011 (<a href="https://arxiv.org/abs/1103.0906v1">v1</a>), last revised 13 Sep 2012 (this version, v5) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1103.0906 | We investigate differential systems occurring in the study of particular non-isolated singularities, the so-called linear free divisors. We obtain a duality theorem for these D-modules taking into account filtrations, and deduce degeneration properties of certain Frobenius manifolds associated to linear sections of the... | math-31-part-1.zip/1103.0906.pdf | |
1903.10116 | On del Pezzo fibrations in positive characteristic | [
"Fabio Bernasconi",
"Hiromu Tanaka"
] | 25 Mar 2019 (<a href="https://arxiv.org/abs/1903.10116v1">v1</a>), last revised 26 Jan 2020 (this version, v3) | 50 pages, v2: minor revisions, v3: minor revisions | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1903.10116 | We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles. Second, we show the existence of purely inseparable sections with explicit bounded degree. To prove these results, we study log del Pezzo ... | math-32-part-2.zip/1903.10116.pdf |
2408.14411 | Positivity of the tangent bundle of rational surfaces with nef anticanonical divisor | [
"Hosung Kim",
"Jeong-Seop Kim",
"Yongnam Lee"
] | 26 Aug 2024 | 20 pages, 14 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2408.14411 | In this paper, we study the property of bigness of the tangent bundle of a smooth projective rational surface with nef anticanonical divisor. We first show that the tangent bundle $T_S$ of $S$ is not big if $S$ is a rational elliptic surface. We then study the property of bigness of the tangent bundle $T_S$ of a weak d... | math-33-part-2.zip/2408.14411.pdf |
1904.07823 | The 0-th Fitting ideal of the Jacobian module of a plane curve | [
"Alexandru Dimca",
"Gabriel Sticlaru"
] | 16 Apr 2019 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.1904.07823 | We describe the 0-th Fitting ideal of the Jacobian module of a plane curve in terms of determinants involving the Jacobian syzygies of this curve. This leads to new characterizations of maximal Tjurina curves, that is of non free plane curves, whose global Tjurina number equals an upper bound given by A. du Plessis and... | math-32-part-2.zip/1904.07823.pdf | |
1903.09006 | Logarithmic Gromov-Witten theory with expansions | [
"Dhruv Ranganathan"
] | 21 Mar 2019 (<a href="https://arxiv.org/abs/1903.09006v1">v1</a>), last revised 2 May 2022 (this version, v3) | 47 pages, 7 figures. v3: Minor changes. Final version to appear in Algebraic Geometry | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1903.09006 | We construct relative Gromov--Witten theory with expanded degenerations in the normal crossings setting and establish a degeneration formula for the resulting invariants. Given a simple normal crossings pair $(X,D)$, we show that there exist proper moduli spaces of curves in $X$ with prescribed boundary conditions alon... | math-32-part-2.zip/1903.09006.pdf |
2312.04677 | Higher Jacobian matrix of weighted homogeneous polynomials and derivation algebras | [
"Wágner Badilla-Céspedes",
"Abel Castorena",
"Daniel Duarte"
] | 7 Dec 2023 (<a href="https://arxiv.org/abs/2312.04677v1">v1</a>), last revised 24 Jul 2025 (this version, v2) | Comments are welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.2312.04677 | We prove that the ideal generated by the maximal minors of the higher-order Jacobian matrix of a weighted homogeneous polynomial is also weighted homogeneous. As an application, we give a partial answer to a conjecture concerning the non-existence of negative weight derivations on the higher Nash blowup local algebra o... | math-33-part-2.zip/2312.04677.pdf |
1701.00413 | $\mathbb{Z}^2$-algebras as noncommutative blow-ups | [
"Dennis Presotto"
] | 2 Jan 2017 (<a href="https://arxiv.org/abs/1701.00413v1">v1</a>), last revised 31 Jul 2017 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1701.00413 | The goal of this note is to first prove that for a well behaved $\mathbb{Z}^2$-algebra $R$, the category $QGr(R) := Gr(R)/Tors(R)$ is equivalent to $QGr(R_\Delta)$ where $R_\Delta$ is a diagonal-like sub-$\mathbb{Z}$-algebra of $R$. Afterwards we use this result to prove that the $\mathbb{Z}^2$-algebras as introduced i... | math-32-part-1.zip/1701.00413.pdf | |
1308.0423 | Rational invariants for subgroups of S_5 and S_7 | [
"Ming-chang Kang",
"Baoshan Wang"
] | 2 Aug 2013 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1308.0423 | Let $G$ be a subgroup of $S_n$, the symmetric group of degree $n$. For any field $k$, $G$ acts naturally on the rational function field $k(x_1,x_2,\ldots,x_n)$ via $k$-automorphisms defined by $\sigma\cdot x_i=x_{\sigma(i)}$ for any $\sigma\in G$, any $1\le i\le n$. Theorem. If $n\le 5$, then the fixed field $k(x_1,\ld... | math-31-part-2.zip/1308.0423.pdf | |
1806.00714 | GW/PT descendent correspondence via vertex operators | [
"Alexei Oblomkov",
"Andrei Okounkov",
"Rahul Pandharipande"
] | 2 Jun 2018 (<a href="https://arxiv.org/abs/1806.00714v1">v1</a>), last revised 8 Apr 2020 (this version, v3) | 36 pages, no pictures; few misprints are corrected; to appear in Communications in Mathematical Physics; slight change in the definition of the generating function for GW invariants; many misprints corrected | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.1806.00714 | We propose an explicit formula for the GW/PT descendent correspondence in the stationary case for nonsingular projective 3-folds. The formula, written in terms of vertex operators, is found by studying the 1-leg geometry. We prove the proposal for all nonsingular projective toric 3-folds. An application to the Virasoro... | math-32-part-2.zip/1806.00714.pdf |
math/0209253 | Counting curves via lattice paths in polygons | [
"Grigory Mikhalkin"
] | 19 Sep 2002 (<a href="https://arxiv.org/abs/math/0209253v1">v1</a>), last revised 5 Apr 2003 (this version, v4) | The version to appear as the English part of a paper in C. R. Acad. Sci. Paris | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO); Geometric Topology (math.GT) | https://doi.org/10.48550/arXiv.math/0209253 | This note presents a formula for the enumerative invariants of arbitrary genus in toric surfaces. The formula computes the number of curves of a given genus through a collection of generic points in the surface. The answer is given in terms of certain lattice paths in the relevant Newton polygon. <br>If the toric surfa... | math-34-part-1.zip/math_0209253.pdf |
1511.09110 | On the functional equations for polylogarithms in one variable | [
"Daniil Rudenko"
] | 2 Nov 2015 | 15 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1511.09110 | We develop a new approach to the study of the functional equations satisfied by classical polylogarithms, inspired by Goncharov's conjectures. We prove a sharpened version of Zagier's criterion for such an equation and explain, how our approach leads to a very simple description of the equations in one variable... | math-32-part-1.zip/1511.09110.pdf |
2012.00272 | Remarks on nef and movable cones of hypersurfaces in Mori dream spaces | [
"Long Wang"
] | 1 Dec 2020 (<a href="https://arxiv.org/abs/2012.00272v1">v1</a>), last revised 18 May 2022 (this version, v4) | v2: The title changed. Add a new result Theorem 1.2 about the cone conjecture. v3: Add Theorem 1.3 about the cone conjecture. v4: Final version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2012.00272 | We investigate nef and movable cones of hypersurfaces in Mori dream spaces. The first result is: Let $Z$ be a smooth Mori dream space of dimension at least four whose extremal contractions are of fiber type of relative dimension at least two and let $X$ be a smooth ample divisor in $Z$, then $X$ is a Mori dream space a... | math-33-part-1.zip/2012.00272.pdf |
0709.2900 | Compactifying normal algebraic spaces | [
"Dan Edidin"
] | 18 Sep 2007 (<a href="https://arxiv.org/abs/0709.2900v1">v1</a>), last revised 20 Sep 2007 (this version, v2) | The author has been informed that the results in this paper were proved by Raoult in 1971. The preprint will remain on the server, but the author makes no claim of originality | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0709.2900 | The author wrote this note after being asked about the existence of compactifications of algebraic spaces. Subsequent to posting the article to the math arXiv, the author learned from Yutakaa Matsuura that the results of this paper had been proved by Raoult in 1971, using the same techniques. Since Raoult's article... | math-30-part-2.zip/0709.2900.pdf |
2309.16132 | Higher Chow cycles on some K3 surfaces with involution | [
"Shouhei Ma",
"Ken Sato"
] | 28 Sep 2023 (<a href="https://arxiv.org/abs/2309.16132v1">v1</a>), last revised 4 Aug 2025 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2309.16132 | We construct, for each 2<r<18, an explicit family of higher Chow cycles of type (2,1) on a family of lattice-polarized K3 surfaces of generic Picard rank r, and prove that the indecomposable part of this cycle is non-torsion for very general members of the family. These are the first explicit examples of such fam... | math-33-part-2.zip/2309.16132.pdf | |
1911.07204 | Genus Two Quasi-Siegel Modular Forms and Gromov-Witten Theory of Toric Calabi-Yau Threefolds | [
"Yongbin Ruan",
"Yingchun Zhang",
"Jie Zhou"
] | 17 Nov 2019 (<a href="https://arxiv.org/abs/1911.07204v1">v1</a>), last revised 13 Nov 2022 (this version, v4) | minor revision. A shortened version to appear in Commun. Math. Phys | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1911.07204 | We first develop theories of differential rings of quasi-Siegel modular and quasi-Siegel Jacobi forms for genus two. Then we apply them to the Eynard-Orantin topological recursion of certain local Calabi-Yau threefolds equipped with branes, whose mirror curves are genus two hyperelliptic curves. By the proof of the Rem... | math-32-part-2.zip/1911.07204.pdf |
1411.5961 | The simplest stationary subalgebras, for compact linear Lie algebras | [
"O. G. Styrt"
] | 21 Nov 2014 | in Russian | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1411.5961 | Sufficient conditions are obtained for the existence of a vector with a one-dimensional or simple three-dimensional stationary subalgebra for an irreducible compact linear Lie algebra. | math-31-part-2.zip/1411.5961.pdf |
2504.02728 | On deformations of Azumaya algebras with quadratic pair | [
"Eoin Mackall",
"Cameron Ruether"
] | 3 Apr 2025 (<a href="https://arxiv.org/abs/2504.02728v1">v1</a>), last revised 8 Apr 2025 (this version, v2) | 50 pages. Added funding information for the second author, otherwise identical to v1 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Rings and Algebras (math.RA) | https://doi.org/10.48550/arXiv.2504.02728 | We construct a tangent-obstruction theory for Azumaya algebras equipped with a quadratic pair. Under the assumption that either 2 is a global unit or the algebra is of degree 2, we show how the deformation theory of these objects reduces to the deformation theory of the underlying Azumaya algebra. Namely, if the underl... | math-33-part-2.zip/2504.02728.pdf |
1109.0612 | Equations describing the ramification of outer simple linear projections | [
"Simon Kurmann"
] | 3 Sep 2011 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1109.0612 | We explain how to determine equations describing the ramification of an outer simple linear projection of a projective scheme in a way suited for explicit computations. | math-31-part-1.zip/1109.0612.pdf | |
1006.4492 | On Invariant Notions of Segre Varieties in Binary Projective Spaces | [
"Hans Havlicek",
"Boris Odehnal",
"Metod Saniga"
] | 23 Jun 2010 (<a href="https://arxiv.org/abs/1006.4492v1">v1</a>), last revised 31 Mar 2011 (this version, v2) | 18 pages, 1 figure; v2 - version accepted in Designs, Codes and Cryptography | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.1006.4492 | Invariant notions of a class of Segre varieties $\Segrem(2)$ of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains $\Segrem(2)$ and is invariant under its projective sta... | math-31-part-1.zip/1006.4492.pdf |
2403.17167 | Monodromy groups of indecomposable coverings of bounded genus | [
"Danny Neftin",
"Michael E. Zieve"
] | 25 Mar 2024 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Group Theory (math.GR); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.2403.17167 | For each nonnegative integer $g$, we classify the ramification types and monodromy groups of indecomposable coverings of complex curves $f: X\to Y$ where $X$ has genus $g$, under the hypothesis that $n:=°(f)$ is sufficiently large and the monodromy group is not $A_n$ or $S_n$. This proves a conjecture of Guralnick and ... | math-33-part-2.zip/2403.17167.pdf | |
1907.08493 | A note on the local Lipschitz triviality of values of complex polynomial functions | [
"Alexandre Fernandes",
"Vincent Grandjean",
"Humberto Soares"
] | 19 Jul 2019 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Metric Geometry (math.MG) | https://doi.org/10.48550/arXiv.1907.08493 | We address the question of the bi-Lipschitz local triviality of a complex polynomial function over a complex value. <br>Our main result state that a non constant complex polynomial admits a locally bi-Lipschitz trivial value if and only if it is a polynomial in a single complex variable. | math-32-part-2.zip/1907.08493.pdf | |
2410.15638 | Hodge symmetry and Lefschetz theorems for singular varieties | [
"Sung Gi Park",
"Mihnea Popa"
] | 21 Oct 2024 (<a href="https://arxiv.org/abs/2410.15638v1">v1</a>), last revised 26 Aug 2025 (this version, v3) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2410.15638 | We prove new results concerning the topology and Hodge theory of singular varieties. A common theme is that concrete conditions on the complexity of the singularities, from a number of different perspectives, are closely related to the symmetries of the Hodge-Du Bois diamond. We relate this to the theory of rational ho... | math-33-part-2.zip/2410.15638.pdf | |
1803.08487 | Log-plurigenera in stable families of surfaces | [
"János Kollár"
] | 22 Mar 2018 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1803.08487 | We study the flatness of log-pluricanonical sheaves on stable families of surfaces. | math-32-part-2.zip/1803.08487.pdf | |
1601.04866 | The Picard group of the universal moduli space of vector bundles on stable curves | [
"Roberto Fringuelli"
] | 19 Jan 2016 (<a href="https://arxiv.org/abs/1601.04866v1">v1</a>), last revised 8 Jun 2018 (this version, v3) | Exposition improved. Comments are welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1601.04866 | We construct the moduli stack of properly balanced vector bundles on semistable curves and we determine explicitly its Picard group. As a consequence, we obtain an explicit description of the Picard groups of the universal moduli stack of vector bundles on smooth curves and of the Schmitt's compactification over th... | math-32-part-1.zip/1601.04866.pdf |
2307.01108 | Perfect-Prismatic F-Crystals and p-adic Shtukas in Families | [
"Anton Güthge"
] | 3 Jul 2023 (<a href="https://arxiv.org/abs/2307.01108v1">v1</a>), last revised 22 Apr 2024 (this version, v2) | Any comments welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2307.01108 | We show an equivalence between the two categories in the title, thus establishing a link between Frobenius-linear objects of formal (schematic) and analytic (adic) nature. We will do this for arbitrary p-complete rings, arbitrary affine-flat group schemes and without making use of the Frobenius structure. As a possible... | math-33-part-2.zip/2307.01108.pdf |
2405.07205 | On embedding of linear hypersurfaces | [
"Parnashree Ghosh",
"Neena Gupta",
"Ananya Pal"
] | 12 May 2024 (<a href="https://arxiv.org/abs/2405.07205v1">v1</a>), last revised 30 Jul 2024 (this version, v3) | This is latest version of the previous article named: On Epimorphism and related problem for linear hypersurfaces | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.2405.07205 | Linear hypersurfaces over a field $k$ have been playing a central role in the study of some of the challenging problems on affine spaces. Breakthroughs on such problems have occurred by examining two difficult questions on linear polynomials of the form $H:=\alpha(X_1,\dots,X_m)Y - F(X_1,\dots, X_m,Z,T)\in D:=k[X_1,\ld... | math-33-part-2.zip/2405.07205.pdf |
0911.0475 | Discriminant coamoebas in dimension two | [
"Lisa Nilsson",
"Mikael Passare"
] | 3 Nov 2009 | 17 pages, 5 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.0911.0475 | This paper deals with coamoebas, that is, images under coordinatewise argument mappings, of certain quite particular plane algebraic curves. These curves are the zero sets of reduced A-discriminants of two variables. We consider the coamoeba primarily as a subset of the torus T^2=(R/2\pi Z)^2, but also as a subset of i... | math-31-part-1.zip/0911.0475.pdf |
2503.05099 | Homotopy Wave Function in Algebraic Geometry | [
"Renaud Gauthier"
] | 7 Mar 2025 | 9 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.2503.05099 | We propose the homotopy shape of the Segal topos of derived stacks over simplicial k-algebras as the higher homotopical generalization of the concept of wave function in Quantum Mechanics | math-33-part-2.zip/2503.05099.pdf |
1705.08846 | On the $μ$-ordinary locus of a Shimura variety | [
"Xuhua He",
"Sian Nie"
] | 24 May 2017 (<a href="https://arxiv.org/abs/1705.08846v1">v1</a>), last revised 12 Jun 2017 (this version, v2) | 13 pages. Introduction expanded | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1705.08846 | In this paper, we study the $\mu$-ordinary locus of a Shimura variety with parahoric level structure. Under the axioms in \cite{HR}, we show that $\mu$-ordinary locus is a union of some maximal Ekedahl-Kottwitz-Oort-Rapoport strata introduced in \cite{HR} and we give criteria on the density of the $\mu$-ordinary locus. | math-32-part-1.zip/1705.08846.pdf |
1608.00376 | On ampleness of canonical bundle | [
"Robert Treger"
] | 1 Aug 2016 (<a href="https://arxiv.org/abs/1608.00376v1">v1</a>), last revised 3 Oct 2017 (this version, v4) | 8 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1608.00376 | We study projective manifolds with nonamenable and non-residually finite fundamental groups. We generalize the uniformization theorem of our earlier note. We generalize a classical theorem of Maltsev about finitely generated subgroups of GL(m). | math-32-part-1.zip/1608.00376.pdf |
1703.06424 | Ulrich Bundles on Projective Spaces | [
"Zhiming Lin"
] | 19 Mar 2017 | 11 pages, 1 figure | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1703.06424 | We assume that $\mathcal{E}$ is a rank $r$ Ulrich bundle for $(P^n, \mathcal{O}(d))$. The main result of this paper is that $\mathcal{E}(i)\otimes \Omega^{j}(j)$ has natural cohomology for any integers $i \in \mathbb{Z}$ and $0 \leq j \leq n$, and every Ulrich bundle $\mathcal{E}$ has a resolution in terms of $n$ of th... | math-32-part-1.zip/1703.06424.pdf |
2506.22897 | Tolerants | [
"Swechchha Adhikari",
"Brent Hall",
"Stephen McKean"
] | 28 Jun 2025 (<a href="https://arxiv.org/abs/2506.22897v1">v1</a>), last revised 7 Jul 2025 (this version, v2) | 13 pages. In this update, we give a resultant formula for the tolerant (answering Question 3.6 from version 1). Comments welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.2506.22897 | We study a generalization of the discriminant of a polynomial, which we call the tolerant. The tolerant differs by a square from the duplicant, which was discovered in recent work on $\mathbb{P}^1$-loop spaces in motivic homotopy theory. We show that the tolerant is rational by deriving a formula in terms of discrimina... | math-33-part-2.zip/2506.22897.pdf |
0912.2623 | On the S-fundamental group scheme II | [
"Adrian Langer"
] | 14 Dec 2009 (<a href="https://arxiv.org/abs/0912.2623v1">v1</a>), last revised 31 Aug 2011 (this version, v3) | v2: simplified proof of the main theorem and added section computing S-fundamental group scheme of a variety with trivial etale fundamental group via Esnault-Mehta method; v3: 20 pages, numerous corrections and clarifications; to appear in J. Inst. Math. Jussieu | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0912.2623 | The S-fundamental group scheme is the group scheme corresponding to the Tannaka category of numerically flat vector bundles. We use determinant line bundles to prove that the S-fundamental group of a product of two complete varieties is a product of their S-fundamental groups as conjectured by V. Mehta and the author. ... | math-31-part-1.zip/0912.2623.pdf |
math/9903066 | Bogomolov's Conjecture for Hyperelliptic Curves over Function Fields | [
"Kazuhiko Yamaki"
] | 12 Mar 1999 | 29 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/9903066 | In this paper, we prove the Effective Bogomolov's Conjecture for hyperelliptic curves defined over function fields. | math-34-part-2.zip/math_9903066.pdf |
1512.02437 | The boundary of the orbit of the 3 by 3 determinant polynomial | [
"Jesko Hüttenhain",
"Pierre Lairez"
] | 8 Dec 2015 (<a href="https://arxiv.org/abs/1512.02437v1">v1</a>), last revised 26 Jul 2016 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1512.02437 | We consider the 3 by 3 determinant polynomial and we describe the limit points of the set of all polynomials obtained from the determinant polynomial by linear change of variables. This answers a question of J. M. Landsberg. | math-32-part-1.zip/1512.02437.pdf | |
1712.05747 | On the Hilbert series of the Grassmannian | [
"Lukas Braun"
] | 15 Dec 2017 | 12 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1712.05747 | We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods and show that its h-polynomial coincides with the k-Narayana polynomial. We give a simplified formula for the h-polynomial of Schubert varieties. Finally, we use a generalized hypergeometric Euler transform to find simplified fo... | math-32-part-2.zip/1712.05747.pdf |
1704.06252 | Finite generation of the numerical Grothendieck group | [
"Goncalo Tabuada"
] | 20 Apr 2017 | 11 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT); K-Theory and Homology (math.KT); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1704.06252 | Let k be a finite base field. In this note, making use of topological periodic cyclic homology and of the theory of noncommutative motives, we prove that the numerical Grothendieck group of every smooth proper dg k-linear category is a finitely generated free abelian group. Along the way, we prove moreover that the cat... | math-32-part-1.zip/1704.06252.pdf |
1803.00799 | Double covers of quadratic degeneracy and Lagrangian intersection loci | [
"Olivier Debarre",
"Alexander Kuznetsov"
] | 2 Mar 2018 (<a href="https://arxiv.org/abs/1803.00799v1">v1</a>), last revised 16 Aug 2019 (this version, v3) | 26 pages. As suggested by Nick Addington, we added an application to double covers of symmetroids. This third version also includes simple but useful additions in Theorem 5.2(2) and 5.7(2), and new Lemmas 3.3 and 4.3 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1803.00799 | We explain a general construction of double covers of quadratic degeneracy loci and Lagrangian intersection loci based on reflexive sheaves. We relate the double covers of quadratic degeneracy loci to the Stein factorizations of the relative Hilbert schemes of linear spaces of the corresponding quadric fibrations. We g... | math-32-part-2.zip/1803.00799.pdf |
0705.2597 | Adelic resolution for homology sheaves | [
"Sergey Gorchinskiy"
] | 17 May 2007 (<a href="https://arxiv.org/abs/0705.2597v1">v1</a>), last revised 11 Feb 2008 (this version, v2) | 64 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); K-Theory and Homology (math.KT) | https://doi.org/10.48550/arXiv.0705.2597 | A generalization of the usual ideles group is proposed, namely, we construct certain adelic complexes for sheaves of $K$-groups on schemes. More generally, such complexes are defined for any abelian sheaf on a scheme. We focus on the case when the sheaf is associated to the presheaf of a homology theory with certain na... | math-30-part-2.zip/0705.2597.pdf |
alg-geom/9502019 | Algebraic cohomology of the moduli space of rank 2 vector bundles on a curve | [
"V. Balaji",
"A.D. King",
"P.E. Newstead"
] | 17 Feb 1995 | 12 pages, Plain TeX with amssym and epsf, 1 figure (eps file appended). Hard copies available | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9502019 | Let $\MC$ be the moduli space of stable holomorphic vector bundles of rank 2 and fixed determinant of odd degree, over a smooth projective curve $C$. This paper identifies the algebraic cohomology ring $\HA^*(\MC)$, i.e. the subring of the rational cohomology ring $H^*(\MC;\QQ)$ spanned by the fundamental classes of al... | small_categories-00.zip/alg-geom_9502019.pdf |
2405.12620 | On the smoothability problem with rational coefficients | [
"Olivier Benoist",
"Claire Voisin"
] | 21 May 2024 (<a href="https://arxiv.org/abs/2405.12620v1">v1</a>), last revised 20 Oct 2024 (this version, v2) | 13 pages, final version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2405.12620 | We consider the problem of smoothing algebraic cycles with rational coefficients on smooth projective complex varieties up to homological equivalence. We show that a solution to this problem would be incompatible with the validity of the Hartshorne conjecture on complete intersections in projective space. We also solve... | math-33-part-2.zip/2405.12620.pdf |
2105.12274 | Toric Richardson varieties of Catalan type and Wedderburn-Etherington numbers | [
"Eunjeong Lee",
"Mikiya Masuda",
"Seonjeong Park"
] | 26 May 2021 (<a href="https://arxiv.org/abs/2105.12274v1">v1</a>), last revised 2 Aug 2022 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.2105.12274 | We associate a complete non-singular fan with a polygon triangulation. Such a fan appears from a certain toric Richardson variety, called of Catalan type introduced in this paper. A toric Richardson variety of Catalan type is a Fano Bott manifold. We show that toric Richardson varieties of Catalan type are classified u... | math-33-part-1.zip/2105.12274.pdf | |
1706.07762 | Tropical refined curve counting from higher genera and lambda classes | [
"Pierrick Bousseau"
] | 23 Jun 2017 (<a href="https://arxiv.org/abs/1706.07762v1">v1</a>), last revised 23 Apr 2019 (this version, v2) | 70 pages, revised version, identical to the one published in Inven. Math | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1706.07762 | Block and Göttsche have defined a $q$-number refinement of counts of tropical curves in $\mathbb{R}^2$. Under the change of variables $q=e^{iu}$, we show that the result is a generating series of higher genus log Gromov-Witten invariants with insertion of a lambda class. This gives a geometric interpretation of the Blo... | math-32-part-1.zip/1706.07762.pdf |
math/9905106 | Deformations of Q-Calabi-Yau 3-folds and Q-Fano 3-folds of Fano index 1 | [
"Tatsuhiro Minagawa"
] | 19 May 1999 | To appear in J. Math. Sci. Univ. Tokyo | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/9905106 | In this article, we prove that any Q-Calabi-Yau 3-fold with only ordinary terminal singularities and any Q-Fano 3-fold of Fano index 1 with only terminal singularities have Q-smoothings. | math-34-part-2.zip/math_9905106.pdf |
math/0106248 | Wild ramification and a vanishing cycles formula | [
"Mohamed Saidi"
] | 28 Jun 2001 | 19 pages amstex, 9 pictures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0106248 | In this paper we prove an explicit formula which compares the dimensions of the spaces of vanishing cycles in a Galois cover of degree p between formal germ of curves over a complete discrete valuation ring of inequal characteristics (0,p). This formula can be easily generalised to the case of a Galois cover with group... | math-34-part-1.zip/math_0106248.pdf |
2410.09242 | Bitangents to symmetric quartics | [
"Candace Bethea",
"Thomas Brazelton"
] | 11 Oct 2024 | 24 pages, comments welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.2410.09242 | Recall that a non-singular planar quartic is a canonically embedded non-hyperelliptic curve of genus three. We say such a curve is symmetric if it admits non-trivial automorphisms. The classification of (necessarily finite) groups appearing as automorphism groups of non-singular curves of genus three dates back to the ... | math-33-part-2.zip/2410.09242.pdf |
1709.03663 | Enumerating Hassett's wall and chamber decomposition of the moduli space of weighted stable curves | [
"Kenneth Ascher",
"Connor Dubé",
"Daniel Gershenson",
"Elaine Hou"
] | 12 Sep 2017 (<a href="https://arxiv.org/abs/1709.03663v1">v1</a>), last revised 11 Jan 2018 (this version, v2) | Minor corrections made and paper reorganized. Version to appear in Experimental Mathematics | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Computational Complexity (cs.CC); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.1709.03663 | Hassett constructed a class of modular compactifications of the moduli space of pointed curves by adding weights to the marked points. This leads to a natural wall and chamber decomposition of the domain of admissible weights where the moduli space and universal family remain constant inside a chamber, and may change u... | math-32-part-1.zip/1709.03663.pdf |
1908.03139 | Closed points on cubic hypersurfaces | [
"Qixiao Ma"
] | 8 Aug 2019 | 11 pages, comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1908.03139 | We generalize some results of Coray on closed points on cubic hypersurfaces. We show certain symmetric products of cubic hypersurfaces are stably birational. | math-32-part-2.zip/1908.03139.pdf |
1512.07145 | On a motivic invariant of the arc-analytic equivalence | [
"Jean-Baptiste Campesato"
] | 22 Dec 2015 (<a href="https://arxiv.org/abs/1512.07145v1">v1</a>), last revised 15 Apr 2016 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1512.07145 | To a Nash function germ, we associate a zeta function similar to the one introduced by J. Denef and F. Loeser. Our zeta function is a formal power series with coefficients in the Grothendieck ring $\mathcal{M}$ of $\mathcal{AS}$-sets up to $\mathbb{R}^*$-equivariant $\mathcal{AS}$-bijections over $\mathbb{R}^*$, an ana... | math-32-part-1.zip/1512.07145.pdf | |
2303.15249 | Computational approach to the Schottky problem | [
"E. Brandon de Leon",
"J. Frauendiener",
"C. Klein"
] | 27 Mar 2023 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.2303.15249 | We present a computational approach to the classical Schottky problem based on Fay's trisecant identity for genus $g\geq 4$. For a given Riemann matrix $\mathbb{B}\in\mathbb{H}^{g}$, the Fay identity establishes linear dependence of secants in the Kummer variety if and only if the Riemann matrix corresponds to a Ja... | math-33-part-2.zip/2303.15249.pdf | |
0706.4184 | Constructing (almost) rigid rings and a UFD having infinitely generated Derksen and Makar-Limanov invariant | [
"David Finston",
"Stefan Maubach"
] | 28 Jun 2007 | Accepted to Canad. Math. Bull | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.0706.4184 | An example is given of a UFD which has infinitely generated Derksen invariant. The ring is \textquotedblleft almost rigid\textquotedblright\ meaning that the Derksen invariant is equal to the Makar-Limanov invariant. Techniques to show that a ring is (almost) rigid are discussed, among which is a generalization of Maso... | math-30-part-2.zip/0706.4184.pdf |
1706.06669 | Metrically un-knotted corank 1 singularities of surfaces in $\mathbb{R}^4$ | [
"Lev Birbrair",
"Rodrigo Mendes",
"Juan Jose Nuño-Ballesteros"
] | 20 Jun 2017 | 10 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1706.06669 | The paper is devoted to relations between topological and metric properties of germs of real surfaces, obtained by analytic maps from $R^2$ to $R^4$. We show that for a big class of such surfaces the normal embedding property implies the triviality of the knot, presenting the link of the surfaces. We also present some ... | math-32-part-1.zip/1706.06669.pdf |
2009.04690 | On tropical cohomology of smooth algebraic varieties | [
"Ryota Mikami"
] | 10 Sep 2020 (<a href="https://arxiv.org/abs/2009.04690v1">v1</a>), last revised 22 Jul 2025 (this version, v6) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2009.04690 | In this paper, we give an explicit description of tropical cohomology of smooth algebraic varieties over trivially valued fields. We also construct ``monodromy weight'' spectral sequences for tropical cohomology of geometric strictly semi-stable reductions. | math-33-part-1.zip/2009.04690.pdf | |
1308.4983 | The effect of points fattening in dimension three | [
"Thomas Bauer",
"Tomasz Szemberg"
] | 22 Aug 2013 (<a href="https://arxiv.org/abs/1308.4983v1">v1</a>), last revised 27 Jan 2014 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1308.4983 | There has been increased recent interest in understanding the relationship between the symbolic powers of an ideal and the geometric properties of the corresponding variety. While a number of results are available for the two-dimensional case, the higher-dimensional case is largely unexplored. In the present paper we s... | math-31-part-2.zip/1308.4983.pdf | |
2010.09165 | Optimal Descartes' Rule of Signs for Circuits | [
"Frédéric Bihan",
"Alicia Dickenstein",
"Jens Forsgård"
] | 19 Oct 2020 (<a href="https://arxiv.org/abs/2010.09165v1">v1</a>), last revised 25 May 2022 (this version, v2) | 21 pages, 5 figures. We improved the proof of Theorem 2.4 by adding Proposition 2.7 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Symbolic Computation (cs.SC) | https://doi.org/10.48550/arXiv.2010.09165 | We present an optimal version of Descartes' rule of signs to bound the number of positive real roots of a sparse system of polynomial equations in n variables with n+2 monomials. This sharp upper bound is given in terms of the sign variation of a sequence associated to the exponents and the coefficients of the syst... | math-33-part-1.zip/2010.09165.pdf |
1204.0123 | Effective Non-vanishing of Asymptotic Adjoint Syzygies | [
"Xin Zhou"
] | 31 Mar 2012 (<a href="https://arxiv.org/abs/1204.0123v1">v1</a>), last revised 8 Apr 2014 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1204.0123 | The purpose of this paper is to establish an effective non-vanishing theorem for the syzygies of an adjoint-type line bundle on a smooth variety, as the positivity of the embedding increases. Our purpose here is to show that for an adjoint type divisor $B = K_X+ bA$ with $b \geq n+1$, one can obtain an effective statem... | math-31-part-2.zip/1204.0123.pdf | |
0808.2749 | An invitation to toric degenerations | [
"Mark Gross",
"Bernd Siebert"
] | 20 Aug 2008 (<a href="https://arxiv.org/abs/0808.2749v1">v1</a>), last revised 23 Jul 2009 (this version, v2) | 41 pages, 21 figures; v2: typos corrected | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.0808.2749 | This is an expository paper which explores the ideas of the authors' paper "From Affine Geometry to Complex Geometry", <a href="https://arxiv.org/abs/0709.2290" data-arxiv-id="0709.2290" class="link-https">arXiv:0709.2290</a>. We explain the basic ideas of the latter paper by going through a large number of... | math-31-part-1.zip/0808.2749.pdf |
0807.3578 | On Ritt's polynomial decomposition theorems | [
"Michael E. Zieve",
"Peter Mueller"
] | 23 Jul 2008 | 38 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.0807.3578 | Ritt studied the functional decomposition of a univariate complex polynomial f into prime (indecomposable) polynomials, f = u_1 o u_2 o ... o u_r. His main achievement was a procedure for obtaining any decomposition of f from any other by repeatedly applying certain transformations. However, Ritt's results provide ... | math-31-part-1.zip/0807.3578.pdf |
1707.00649 | Prime-to-$p$ étale fundamental groups of punctured projective lines over strictly Henselian fields | [
"Hilaf Hasson",
"Jeffrey Yelton"
] | 3 Jul 2017 (<a href="https://arxiv.org/abs/1707.00649v1">v1</a>), last revised 22 Jun 2020 (this version, v4) | 18 pages, 4 sections, 20 sources cited. This version is the result of major revisions as suggested by a referee; in particular sections 3 and 4 have switched places. This is the form of the article appearing in Transactions of the American Mathematical Society | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1707.00649 | Let $K$ be the fraction field of a strictly Henselian DVR of characteristic $p \geq 0$ with algebraic closure $\bar{K}$, and let $\alpha_{1}, ..., \alpha_{d} \in \mathbb{P}_{K}^{1}(K)$. In this paper, we give explicit generators and relations for the prime-to-$p$ étale fundamental group of $\mathbb{P}_K^1\smallsetminus... | math-32-part-1.zip/1707.00649.pdf |
0905.0342 | Non-vanishing forms in projective space over finite fields | [
"Samuel Lundqvist"
] | 4 May 2009 (<a href="https://arxiv.org/abs/0905.0342v1">v1</a>), last revised 25 May 2015 (this version, v2) | 6 pages. Citations are updated and a section on how to compute a non-vanishing form is added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.0905.0342 | We consider a subset of projective space over a finite field and give bounds on the minimal degree of a non-vanishing form with respect to this subset. | math-31-part-1.zip/0905.0342.pdf |
0808.2522 | Unification theorems in algebraic geometry | [
"E. Daniyarova",
"A. Myasnikov",
"V. Remeslennikov"
] | 19 Aug 2008 | 28 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Logic (math.LO) | https://doi.org/10.48550/arXiv.0808.2522 | In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along the way we lay down foundations of algebraic geometry over arbitrary algebraic str... | math-31-part-1.zip/0808.2522.pdf |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.