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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1112.2191 | The Lefschetz-Lunts formula for deformation quantization modules | [
"Francois Petit"
] | 9 Dec 2011 (<a href="https://arxiv.org/abs/1112.2191v1">v1</a>), last revised 22 Jan 2013 (this version, v2) | 19 pages; Mathematische Zeitschrift 2012 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1112.2191 | We adapt to the case of deformation quantization modules a formula of V. Lunts who calculates the trace of a kernel acting on Hochschild homology. | math-31-part-2.zip/1112.2191.pdf |
math/0111168 | A strange example concerning Property N_p | [
"Elena Rubei"
] | 14 Nov 2001 | 3 pages, latex | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.math/0111168 | We exhibit an example of a line bundle M on a smooth complex projective variety Y s.t. M satisfy Property N_p for some p, the p-module of a minimal resolution of the ideal of the embedding of Y by M is nonzero and M^2 does not satisfy Property N_p. | math-34-part-1.zip/math_0111168.pdf |
1612.01583 | Monodromy of the $SL(n)$ and $GL(n)$ Hitchin fibrations | [
"David Baraglia"
] | 5 Dec 2016 | 32 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Differential Geometry (math.DG) | https://doi.org/10.48550/arXiv.1612.01583 | We compute the monodromy of the Hitchin fibration for the moduli space of $L$-twisted $SL(n,\mathbb{C})$ and $GL(n,\mathbb{C})$-Higgs bundles for any $n$, on a compact Riemann surface of genus $g>1$. We require the line bundle $L$ to either be the canonical bundle or satisfy $deg(L) > 2g-2$. The monodromy group i... | math-32-part-1.zip/1612.01583.pdf |
2310.07340 | Tame deformations of highly singular function germs | [
"Cezar Joiţa",
"Matteo Stockinger",
"Mihai Tibăr"
] | 11 Oct 2023 (<a href="https://arxiv.org/abs/2310.07340v1">v1</a>), last revised 13 Mar 2025 (this version, v3) | final version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.2310.07340 | We give analytic and algebraic conditions under which a deformation of real analytic functions with non-isolated singular locus is a deformation with fibre constancy. | math-33-part-2.zip/2310.07340.pdf |
math/0605343 | Recursive formula for psi^g - lambda_1 psi^{g-1} + ... + (-1)^g lambda_g in \Mbar_{g,1} | [
"D. Arcara",
"F. Sato"
] | 12 May 2006 | 5 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0605343 | Mumford proved that psi^g - lambda_1 psi^{g-1} + ... + (-1)^g lambda_g = 0 in the Chow ring of M_{g,1} [Mum83]. We find an explicit recursive formula for psi^g - lambda_1 psi^{g-1} + ... + (-1)^g lambda_g in the tautological ring of \Mbar_{g,1} as a combination of classes supported on boundary strata. | math-34-part-1.zip/math_0605343.pdf |
math/0609811 | Fixed points of automorphisms of real algebraic curves | [
"Jean-Philippe Monnier"
] | 28 Sep 2006 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0609811 | We bound the number of fixed points of an automorphism of a real curve in terms of the genus and the number of connected components of the real part of the curve. Using this bound, we derive some consequences concerning the maximum order of an automorphism and the maximum order of an abelian group of automorphisms of a... | math-34-part-1.zip/math_0609811.pdf | |
2211.12319 | A Tensor Restriction Theorem over Finite Fields | [
"Andreas Blatter",
"Jan Draisma",
"Filip Rupniewski"
] | 22 Nov 2022 | 31 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2211.12319 | Restriction is a natural quasi-order on $d$-way tensors. We establish a remarkable aspect of this quasi-order in the case of tensors over a fixed finite field -- namely, that it is a well-quasi-order: it admits no infinite antichains and no infinite strictly decreasing sequences. This result, reminiscent of the graph m... | math-33-part-1.zip/2211.12319.pdf |
1802.09039 | Flag bundles, Segre polynomials and push-forwards | [
"Lionel Darondeau",
"Piotr Pragacz"
] | 25 Feb 2018 | The content of this paper was presented by Piotr Pragacz at the International Festival in Schubert Calculus in Guangzhou, November 6-10, 2017 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1802.09039 | In this note, we give Gysin formulas for partial flag bundles for the classical groups. We then give Gysin formulas for Schubert varieties in Grassmann bundles, including isotropic ones. All these formulas are proved in a rather uniform way by using the step-by-step construction of flag bundles and the Gysin formula fo... | math-32-part-2.zip/1802.09039.pdf |
2307.06014 | The Waldschmidt constant of a standard $\Bbbk$-configuration in $\mathbb P^2$ | [
"Maria Virginia Catalisano",
"Giuseppe Favacchio",
"Elena Guardo",
"Yong-Su Shin"
] | 12 Jul 2023 (<a href="https://arxiv.org/abs/2307.06014v1">v1</a>), last revised 27 Jul 2023 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.2307.06014 | A $\Bbbk$-configuration of type $(d_1,\dots,d_s)$ is a specific set of points in $\mathbb P^2$ that has a number of algebraic and geometric properties. For example, the graded Betti numbers and Hilbert functions of all $\Bbbk$-configurations in $\mathbb P^2$ are determined by the type $(d_1,\dots,d_s)$. However the Wal... | math-33-part-2.zip/2307.06014.pdf | |
1611.06074 | A note on distinguished bases of singularities | [
"Wolfgang Ebeling"
] | 18 Nov 2016 (<a href="https://arxiv.org/abs/1611.06074v1">v1</a>), last revised 12 Jun 2017 (this version, v2) | 13 pages, 7 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1611.06074 | For an isolated hypersurface singularity which is neither simple nor simple elliptic, it is shown that there exists a distinguished basis of vanishing cycles which contains two basis elements with an arbitrary intersection number. This implies that the set of Coxeter-Dynkin diagrams of such a singularity is infinite, w... | math-32-part-1.zip/1611.06074.pdf |
2208.00217 | Birational involutions of the real projective plane | [
"Ivan Cheltsov",
"Frédéric Mangolte",
"Egor Yasinsky",
"Susanna Zimmermann"
] | 30 Jul 2022 (<a href="https://arxiv.org/abs/2208.00217v1">v1</a>), last revised 10 May 2024 (this version, v2) | Minor corrections following referees' comments. To appear in J. Eur. Math. Soc. (JEMS) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2208.00217 | We classify birational involutions of the real projective plane up to conjugation. In contrast with an analogous classification over the complex numbers (due to E. Bertini, G. Castelnuovo, F. Enriques, L. Bayle and A. Beauville), which includes 4 different classes of involutions, we discover 12 different classes over t... | math-33-part-1.zip/2208.00217.pdf |
0804.4047 | Fourier-Mukai partners of a K3 surface and the cusps of its Kahler moduli | [
"Shouhei Ma"
] | 25 Apr 2008 (<a href="https://arxiv.org/abs/0804.4047v1">v1</a>), last revised 22 Aug 2008 (this version, v3) | 25 pages. I corrected a mistake | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.0804.4047 | Using lattice theory, we establish a one-to-one correspondence between the set of Fourier-Mukai partners of a projective $K3$ surface and the set of 0-dimensional standard cusps of its Kahler moduli. We also study the relation between twisted Fourier-Mukai partners and general 0-dimensional cusps, and the relation betw... | math-31-part-1.zip/0804.4047.pdf |
0802.2338 | On non Fundamental Group Equivalent Surfaces | [
"Michael Friedman",
"Mina Teicher"
] | 16 Feb 2008 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0802.2338 | In this paper we present an example of two polarized K3 surfaces which are not Fundamental Group Equivalent (their fundamental groups of the complement of the branch curves are not isomorphic; denoted by FGE) but the fundamental groups of their related Galois covers are isomorphic. For each surface, we consider a gener... | math-31-part-1.zip/0802.2338.pdf | |
1305.2549 | The Hodge filtration on complements of complex coordinate subspace arrangements and integral representations of holomorphic functions | [
"Yury Eliyashev"
] | 12 May 2013 | 13 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1305.2549 | We compute the Hodge filtration on cohomology groups of complements of complex coordinate subspace arrangements. By means of this result we construct integral representations of holomorphic functions such that kernels of these representations have singularities on complex coordinate subspace arrangements. | math-31-part-2.zip/1305.2549.pdf |
1210.3249 | Calabi-Yau conifold expansions | [
"Slawomir Cynk",
"Duco van Straten"
] | 11 Oct 2012 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1210.3249 | We describe examples of computations of Picard-Fuchs operators for families of Calabi-Yau manifolds based on the expansion of a period near a conifold point. We find examples of operators without a point of maximal unipotent monodromy, thus answering a question posed by J. Rohde. | math-31-part-2.zip/1210.3249.pdf | |
2011.07300 | Inversion of adjunction for quotient singularities | [
"Yusuke Nakamura",
"Kohsuke Shibata"
] | 14 Nov 2020 (<a href="https://arxiv.org/abs/2011.07300v1">v1</a>), last revised 30 Jul 2021 (this version, v2) | 38 pages. To appear in Algebraic Geometry | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2011.07300 | We prove the precise inversion of adjunction formula for quotient singularities and klt Cartier divisors. As an application, we prove the semi-continuity of minimal log discrepancies for klt hyperquotient singularities. | math-33-part-1.zip/2011.07300.pdf |
2406.19506 | Symmetric powers of null motivic Euler characteristic | [
"Dori Bejleri",
"Stephen McKean"
] | 27 Jun 2024 (<a href="https://arxiv.org/abs/2406.19506v1">v1</a>), last revised 6 Jan 2025 (this version, v2) | 45 pages, 1 figure. Updated with a few minor corrections. Comments welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.2406.19506 | Let k be a field of characteristic not 2. We conjecture that if X is a quasi-projective k-variety with trivial motivic Euler characteristic, then Sym$^n$X has trivial motivic Euler characteristic for all n. Conditional on this conjecture, we show that the Grothendieck--Witt ring admits a power structure that is compati... | math-33-part-2.zip/2406.19506.pdf |
1605.03929 | A note on the automorphism group of Schubert varieties | [
"Fernando Piñero"
] | 12 May 2016 (<a href="https://arxiv.org/abs/1605.03929v1">v1</a>), last revised 8 Jan 2017 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1605.03929 | In this work we extend some previously known results on the automorphism group of Schubert varieties. We consider the Schubert conditions which define a Schubert variety. An automorphism of the Grassmannian fixes a Schubert variety contained in it if and only if it fixes certain elements of the flag used to define the ... | math-32-part-1.zip/1605.03929.pdf | |
0812.2662 | Equivariant Lie-Rinehart cohomology | [
"Eivind Eriksen",
"Trond S. Gustavsen"
] | 14 Dec 2008 | 7 pages, LaTeX, based on a talk I gave at the AGMF Baltic-Nordic Workshop in Tartu, 9-11 October, 2008 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Rings and Algebras (math.RA) | https://doi.org/10.48550/arXiv.0812.2662 | In this paper, we study Lie-Rinehart cohomology for quotients of singularities by finite groups, and interpret these cohomology groups in terms of integrable connection on modules. | math-31-part-1.zip/0812.2662.pdf |
1606.06615 | On the Milnor monodromy of the exceptional reflection arrangement of type $G_{31}$ | [
"Alexandru Dimca",
"Gabriel Sticlaru"
] | 21 Jun 2016 (<a href="https://arxiv.org/abs/1606.06615v1">v1</a>), last revised 27 Dec 2017 (this version, v3) | v3. Minor changes in the presentation. Most of the Singular codes used in the paper are available now on the webpage of the first author | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Group Theory (math.GR) | https://doi.org/10.48550/arXiv.1606.06615 | Combining recent results by A. Macinic, S. Papadima and R. Popescu with a spectral sequence and computer aided computations, we determine the monodromy action on $H^1(F,\mathbb{C})$, where $F$ denotes the Milnor fiber of the hyperplane arrangement associated to the exceptional irreducible complex reflection group $G_{3... | math-32-part-1.zip/1606.06615.pdf |
2104.14947 | A Hurwitz divisor on the Moduli of Prym curves | [
"Andrei Bud"
] | 30 Apr 2021 (<a href="https://arxiv.org/abs/2104.14947v1">v1</a>), last revised 18 Feb 2024 (this version, v3) | Final version. Accepted in Geometriae Dedicata | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2104.14947 | For genus $g=2i\geq4$ and the length $g-1$ partition $\mu = (4,2,\ldots,2,-2,\ldots,-2)$ of 0, we compute the first coefficients of the class of $\overline{D}(\mu)$ in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{R}}_g)$, where $D(\mu)$ is the divisor consisting of pairs $[C,\eta]\in \mathcal{R}_g$ with $\eta \cong \mat... | math-33-part-1.zip/2104.14947.pdf |
1604.03464 | Approximation forte pour les espaces homogènes de groupes semisimples sur le corps des fonctions d'une courbe algébrique complexe | [
"Jean-Louis Colliot-Thélène"
] | 12 Apr 2016 (<a href="https://arxiv.org/abs/1604.03464v1">v1</a>), last revised 19 Apr 2016 (this version, v2) | Title changed, arbitrary homogeneous spaces now handled, in French | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Group Theory (math.GR) | https://doi.org/10.48550/arXiv.1604.03464 | Let K be the function field of a curve over the complex field. Let X be a homogeneous space of a semisimple linear algebraic group. Strong approximation holds for X outside any finite nonempty set of places of K. Strong approximation fails for tori over K. | math-32-part-1.zip/1604.03464.pdf |
2506.12438 | Gromov-Witten theory of $\mathsf{Hilb}^n(\mathbb{C}^2)$ and Noether-Lefschetz theory of $\mathcal{A}_g$ | [
"Aitor Iribar Lopez",
"Rahul Pandharipande",
"Hsian-Hua Tseng"
] | 14 Jun 2025 (<a href="https://arxiv.org/abs/2506.12438v1">v1</a>), last revised 30 Aug 2025 (this version, v2) | 40 pages, updated bibliography | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2506.12438 | We calculate the genus 1 Gromov-Witten theory of the Hilbert scheme $\mathsf{Hilb}^n(\mathbb{C}^2)$ of points in the plane. The fundamental 1-point invariant (with a divisor insertion) is calculated using a correspondence with the families local curve Gromov-Witten theory over the moduli space $\overline{\mathcal{M}}_{... | math-33-part-2.zip/2506.12438.pdf |
1501.02984 | Remarks and questions on coisotropic subvarieties and 0-cycles of hyper-Kähler varieties | [
"Claire Voisin"
] | 13 Jan 2015 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1501.02984 | This paper proposes a conjectural picture for the structure of the Chow ring of a (projective) hyper-Kähler variety, and the construction of a Beauville decomposition, with emphasis on the Chow group of $0$-cycles, which is endowed with a natural filtration of Brill-Noether type. Some of the conjectures are proved in t... | math-31-part-2.zip/1501.02984.pdf | |
1609.00454 | Brauer group of moduli of Higgs bundles and connections | [
"David Baraglia",
"Indranil Biswas",
"Laura P. Schaposnik"
] | 2 Sep 2016 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV); Geometric Topology (math.GT) | https://doi.org/10.48550/arXiv.1609.00454 | Given a compact Riemann surface $X$ and a semisimple affine algebraic group $G$ defined over $\mathbb C$, there are moduli spaces of Higgs bundles and of connections associated to $(X,\, G)$. We compute the Brauer group of the smooth locus of these varieties. | math-32-part-1.zip/1609.00454.pdf | |
2212.14375 | Smooth Compactifications of the Abel-Jacobi Section | [
"Sam Molcho"
] | 29 Dec 2022 (<a href="https://arxiv.org/abs/2212.14375v1">v1</a>), last revised 22 Jan 2023 (this version, v2) | 30 pages. Comments and suggestions welcome. v2: Fixed a broken reference, some minor rewording in the introduction | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2212.14375 | For $\theta$ a small generic universal stability condition of degree $0$ and $A$ a vector of integers adding up to $k(2g-2)$, the spaces $\overline{M}_{g,n}^\theta$ resolving the Abel-Jacobi section to the compactified Jacobian Pic^\theta constructed in the work of Abreu-Pacini and Holmes-Molcho-Pandharipande-Pixton-Sc... | math-33-part-1.zip/2212.14375.pdf |
2403.19715 | Equivariant toric geometry and Euler-Maclaurin formulae -- an overview | [
"Sylvain E. Cappell",
"Laurenţiu Maxim",
"Jörg Schürmann",
"Julius L. Shaneson"
] | 27 Mar 2024 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2403.19715 | We survey recent developments in the study of torus equivariant motivic Chern and Hirzebruch characteristic classes of projective toric varieties, with applications to calculating equivariant Hirzebruch genera of torus-invariant Cartier divisors in terms of torus characters, as well as to general Euler-Maclaurin type f... | math-33-part-2.zip/2403.19715.pdf | |
alg-geom/9501009 | On the Hilbert scheme of curves in higher-dimensional projective space | [
"Barbara Fantechi",
"Rita Pardini"
] | 17 Jan 1995 | latex, 12 pages, no figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9501009 | In this paper we prove that, for any $n\ge 3$, there exist infinitely many $r\in \N$ and for each of them a smooth, connected curve $C_r$ in $¶^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme $\hilb(¶^r)$. This is proven by reducing the problem to an analogous statement for the modul... | small_categories-00.zip/alg-geom_9501009.pdf |
2102.12246 | Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces | [
"David Alfaya",
"André Oliveira"
] | 24 Feb 2021 (<a href="https://arxiv.org/abs/2102.12246v1">v1</a>), last revised 4 Apr 2024 (this version, v5) | 67 pages, 1 figure | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2102.12246 | Let $\mathcal{L}=(L,[\cdot\,,\cdot],\delta)$ be an algebraic Lie algebroid over a smooth projective curve $X$ of genus $g\geq 2$ such that $L$ is a line bundle whose degree is less than $2-2g$. Let $r$ and $d$ be coprime numbers. We prove that the motivic class of the moduli space of $\mathcal{L}$-connections of rank $... | math-33-part-1.zip/2102.12246.pdf |
0707.3268 | Characteristic classes of the Hilbert schemes of points on non-compact simply-connected surfaces | [
"Marc Nieper-Wisskirchen"
] | 22 Jul 2007 | 8 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.0707.3268 | We prove a closed formula expressing any multiplicative characteristic class evaluated on the tangent bundle of the Hilbert schemes of points on a non-compact simply-connected surface. <br>As a corollary, we deduce a closed formula for the Chern character of the tangent bundles of these Hilbert schemes. <br>We also giv... | math-30-part-2.zip/0707.3268.pdf |
1703.07299 | Differential uniformity and second order derivatives for generic polynomials | [
"Yves Aubry",
"Fabien Herbaut"
] | 21 Mar 2017 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.1703.07299 | For any polynomial $f$ of ${\mathbb F}\_{2^n}[x]$ we introduce the following characteristic of the distribution of its second order derivative,which extends the differential uniformity notion:$$\delta^2(f):=\max\_{\substack{\alpha \in {\mathbb F}\_{2^n}^{\ast} ,\alpha' \in {\mathbb F}\_{2^n}^{\ast} ,\beta \in {\mat... | math-32-part-1.zip/1703.07299.pdf | |
2408.15155 | Relative Fundamental Lemmas for Spherical Hecke Algebras and Multiplicative Hitchin Fibrations: the Jacquet--Rallis Case | [
"X. Griffin Wang",
"Zhiyu Zhang"
] | 27 Aug 2024 (<a href="https://arxiv.org/abs/2408.15155v1">v1</a>), last revised 19 Sep 2024 (this version, v2) | 70 pages; added some background information and a few references | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.2408.15155 | We prove the Jacquet--Rallis fundamental lemma for spherical Hecke algebras over local function fields using multiplicative Hitchin fibrations. Our work is inspired by the proof of [Yun11] in the Lie algebra case and builds upon the general framework of multiplicative Hitchin fibrations in [Wang24]. | math-33-part-2.zip/2408.15155.pdf |
1405.1394 | Essential dimension, stable cohomological dimension, and stable cohomology of finite Heisenberg groups | [
"Fedor Bogomolov",
"Christian Böhning"
] | 6 May 2014 | 18 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1405.1394 | We compare the notions of essential dimension and stable cohomological dimension of a finite group G, prove that the latter is bounded by the length of any normal series with cyclic quotients for G, and show that, however, this bound is not sharp by showing that the stable cohomological dimension of the finite Heisenbe... | math-31-part-2.zip/1405.1394.pdf |
math/0304352 | Raynaud's group-scheme and reduction of coverings | [
"Dan Abramovich",
"Jonathan Lubin"
] | 23 Apr 2003 (<a href="https://arxiv.org/abs/math/0304352v1">v1</a>), last revised 4 Jan 2006 (this version, v2) | Results much improved thanks to computations of Romagny, hopefully leading to complete moduli space in joint work in the near future. Added appendix by Lubin, of which this is the fun version. If you want to see the master working in Lubin Tate theory read this - the published version, he threatens, will be cut and dry | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0304352 | The structure of the reduction of an admissible $G$-covering $Y \to X$ at primes $p$ dividing $|G|$ is investigated. Assume $|G|$ is not divisible by $p^2$ and the $p$-Sylow group is normal. Following Raynaud it is shown that there is a group scheme $\cG$ over the smooth locus of $X$ for which $Y$ is still a principal ... | math-34-part-1.zip/math_0304352.pdf |
1201.5766 | Completion theorem for equivariant $K$-theory | [
"Amalendu Krishna"
] | 27 Jan 2012 (<a href="https://arxiv.org/abs/1201.5766v1">v1</a>), last revised 16 Nov 2015 (this version, v2) | Final version, to appear in J. reine angew. Math. (Crelle), (2015) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); K-Theory and Homology (math.KT) | https://doi.org/10.48550/arXiv.1201.5766 | In this paper, we study the algebraic analogue of the topological Atiyah-Segal completion theorem. We verify this completion theorem for the algebraic equivariant $K$-theory of smooth projective schemes. We also show that the completion theorem fails in general for smooth non-projective schemes. | math-31-part-2.zip/1201.5766.pdf |
2203.03424 | Multiplicity algebras for rank 2 bundles on curves of small genus | [
"Nigel Hitchin"
] | 7 Mar 2022 (<a href="https://arxiv.org/abs/2203.03424v1">v1</a>), last revised 5 Oct 2022 (this version, v2) | Dedicated to Oscar Garcia-Prada on the occasion of his 60th birthday | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2203.03424 | Hausel introduced a commutative algebra -- the multiplicity algebra -- associated to a fixed point of the C^*-action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector bundle and zero Higgs field for a curve of low genus. Geometrically, the relati... | math-33-part-1.zip/2203.03424.pdf |
2507.06882 | Moduli spaces of stable bundles on ruled 3-folds and Brill-Noether problems | [
"Laura Costa",
"Irene Macías Tarrío"
] | 9 Jul 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2507.06882 | In this paper, we redefine the theory of walls and chambers due to Qin developing a new tool to study moduli spaces of stable rank 2 vector bundles on algebraic varieties of higher dimension. We apply it to describe components of some moduli spaces of rank 2 stable bundles on ruled 3-folds as well as to prove that some... | math-34-part-1.zip/2507.06882.pdf | |
1410.0466 | Brauer groups for quiver moduli | [
"Markus Reineke",
"Stefan Schroeer"
] | 2 Oct 2014 | 20 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.1410.0466 | We compute the Brauer groups of several moduli spaces of stable quiver representations. | math-31-part-2.zip/1410.0466.pdf |
1011.6131 | Alpha invariant and K-stability of Q-Fano varieties | [
"Yuji Odaka",
"Yuji Sano"
] | 29 Nov 2010 (<a href="https://arxiv.org/abs/1011.6131v1">v1</a>), last revised 8 Aug 2012 (this version, v2) | Final version (published) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Differential Geometry (math.DG) | https://doi.org/10.48550/arXiv.1011.6131 | We give a purely algebro-geometric proof that if the alpha-invariant of a Q-Fano variety X is greater than dim X/(dim X+1), then (X,O(-K_X)) is K-stable. The key of our proof is a relation among the Seshadri constants, the alpha-invariant and K-stability. It also gives applications concerning the automorphism group. | math-31-part-1.zip/1011.6131.pdf |
0807.3257 | Positive Polynomials and Sequential Closures of Quadratic Modules | [
"Tim Netzer"
] | 21 Jul 2008 | 21 pages, 3 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0807.3257 | Let S be a basic closed semi-algebraic set in R^n and P the corresponding preordering in R[X_1,...,X_n]. We examine for which polynomials f there exist identities f+\ep q \in P for all \ep>0. These are precisely the elements of the sequential closure of P with respect to the finest locally convex topology. We solve ... | math-31-part-1.zip/0807.3257.pdf |
math/9801005 | Stable maps of genus zero to flag spaces | [
"Yu. I. Manin"
] | 2 Jan 1998 (<a href="https://arxiv.org/abs/math/9801005v1">v1</a>), last revised 9 Dec 1998 (this version, v2) | 12 pages, AMSTex. Several annoying misprints and errors in formulas are corrected | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Quantum Algebra (math.QA) | https://doi.org/10.48550/arXiv.math/9801005 | We calculate a generating series for the virtual Euler-Poincaré characteristics of the spaces of stable maps of genus zero to flag spaces using the summation over trees technique. | math-34-part-2.zip/math_9801005.pdf |
math/0610269 | Orbifold Cohomology of A Wreath Product Orbifold | [
"Tomoo Matsumura"
] | 9 Oct 2006 (<a href="https://arxiv.org/abs/math/0610269v1">v1</a>), last revised 26 Nov 2006 (this version, v2) | Version 2: minor changes, with some errors corrected and references modified | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0610269 | Let X be a compact almost complex manifold with an action of a finite group G. We compute the algebra of G^n coinvariants of the stringy cohomology (<a href="https://arxiv.org/abs/math.AG/0104207" data-arxiv-id="math.AG/0104207" class="link-https">math.AG/0104207</a>) of X^n with an action of a wreath product of G. We ... | math-34-part-1.zip/math_0610269.pdf |
1104.1782 | Cubic Surfaces with Special Periods | [
"James A. Carlson",
"Domingo Toledo"
] | 10 Apr 2011 (<a href="https://arxiv.org/abs/1104.1782v1">v1</a>), last revised 5 Oct 2011 (this version, v3) | Implemented the referees thoughtful comments and suggestions. Thankyou! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1104.1782 | We show that the vector of period ratios of a cubic surface is rational over $Q(\omega)$, where $\omega = \exp(2\pi i/3)$ if and only if the associate abelian variety is isogeneous to a product of Fermat elliptic curves. We also show how to construct cubic surfaces from a suitable totally real quintic number field $K_0... | math-31-part-1.zip/1104.1782.pdf |
math/0302045 | Classification of quadruple Galois canonical covers I | [
"Francisco J. Gallego",
"B. P. Purnaprajna"
] | 5 Feb 2003 (<a href="https://arxiv.org/abs/math/0302045v1">v1</a>), last revised 8 Dec 2003 (this version, v2) | 24 Pages, AMSTeX. This version contains a significant amount of new results and material. A part of the material and results from the older version have been removed and will appear, along with new results, in a second part to this paper, which will be posted subsequently | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0302045 | In this article we classify quadruple Galois canonical covers of smooth surfaces of minimal degree. The classification shows that they are either non-simple cyclic covers or bi-double covers. <br>If they are bi-double then they are all fiber products of double covers. We construct examples to show that all the possibil... | math-34-part-1.zip/math_0302045.pdf |
2506.09828 | Continuity of the superpotentials and slices of tropical currents | [
"Farhad Babaee",
"Tien Cuong Dinh"
] | 11 Jun 2025 | 35 pages, 1 figure | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO); Dynamical Systems (math.DS) | https://doi.org/10.48550/arXiv.2506.09828 | We study the question of the continuity of slices of currents and explain how it relates to several seemingly unrelated problems in tropical geometry. On the one hand, through this lens, we show that the continuity of superpotentials constitutes a very general instance of stable intersection theory in tropical geometry... | math-33-part-2.zip/2506.09828.pdf |
math/0212044 | Toric ideals, real toric varieties, and the algebraic moment map | [
"Frank Sottile"
] | 3 Dec 2002 (<a href="https://arxiv.org/abs/math/0212044v1">v1</a>), last revised 18 Apr 2008 (this version, v3) | Corrected the discussion in the published version about the moment map, and changed the title from "Toric ideals, real toric varieties, and the moment map". This should be the definitive version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Computational Geometry (cs.CG) | https://doi.org/10.48550/arXiv.math/0212044 | This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties and the algebraic moment map. In particular, we explain the relation between linear precision and the algebraic moment map. ... | math-34-part-1.zip/math_0212044.pdf |
0804.1491 | Remarks on a normal subgroup of GA_n | [
"Jakub Zygadło"
] | 9 Apr 2008 | 5 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Group Theory (math.GR) | https://doi.org/10.48550/arXiv.0804.1491 | We show that the subgroup generated by locally finite polynomial automorphisms of k^n is normal in GA_n. Also, some properties of normal subgroups of GA_n containing all diagonal automorphisms are given. | math-31-part-1.zip/0804.1491.pdf |
1306.0163 | A Characterization of Mumford Curves with Good Reduction | [
"Jie Xia"
] | 2 Jun 2013 | 18 pages. Comments welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1306.0163 | Mumford defines a certain type of Shimura curves of Hodge type, parameterizing polarized complex abelian fourfolds. In this paper, we study the good reduction of such a curve in positive characteristic and give a characterization in the generically ordinary case. | math-31-part-2.zip/1306.0163.pdf |
1602.06427 | Correspondence between 2 Calabi-Yau Categories and Quivers | [
"Jie Ren"
] | 20 Feb 2016 (<a href="https://arxiv.org/abs/1602.06427v1">v1</a>), last revised 9 Jan 2020 (this version, v2) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1602.06427 | This note gives a one-to-one correspondence between the equivalence classes of a certain type of 2-dimensional Calabi-Yau categories, and certain type of quivers, This is an analogue of the result in Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, arXiv: <a href="https://arxiv.org... | math-32-part-1.zip/1602.06427.pdf | |
2409.04735 | Counting points on generic character varieties | [
"Masoud Kamgarpour",
"GyeongHyeon Nam",
"Bailey Whitbread",
"Stefano Giannini"
] | 7 Sep 2024 (<a href="https://arxiv.org/abs/2409.04735v1">v1</a>), last revised 3 Mar 2025 (this version, v2) | The paper has been re-written to make the exposition better. Additional examples are added to illustrate the main results. Computer calculations are provided to support the purity conjecture | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.2409.04735 | We count points on character varieties associated with punctured surfaces and regular semisimple generic conjugacy classes in reductive groups. We find that the number of points are palindromic polynomials. This suggests a $P=W$ conjecture for these varieties. We also count points on the corresponding additive characte... | math-33-part-2.zip/2409.04735.pdf |
2406.19782 | Generically nonreduced components of Hilbert schemes on fourfolds | [
"Joachim Jelisiejew"
] | 28 Jun 2024 | Comments welcome! To appear in a special volume of Rendiconti del seminario matematico di Torino dedicated to Gianfranco Casnat | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.2406.19782 | We exhibit generically nonreduced components of the Hilbert scheme of at least $21$ points on a smooth variety of dimension at least four. The result was announced in~[Jelisiejew__open_problems] and answers a question~[Problem~3.8, AIMPL]. The method is similar to the one of~[\S6, Jelisiejew-Šivic]. | math-33-part-2.zip/2406.19782.pdf |
0908.0522 | Fermat hypersurfaces and Subcanonical curves | [
"Pietro De Poi",
"Francesco Zucconi"
] | 4 Aug 2009 (<a href="https://arxiv.org/abs/0908.0522v1">v1</a>), last revised 29 Apr 2011 (this version, v4) | 18 pages; AMS-LaTeX | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.0908.0522 | We extend the classical Enriques-Petri Theorem to $s$-subcanonical projectively normal curves, proving that such a curve is $(s+2)$-gonal if and only if it is contained in a surface of minimal degree. Moreover, we show that any Fermat hypersurface of degree $s+2$ is apolar to an $s$-subcanonical $(s+2)$-gonal projectiv... | math-31-part-1.zip/0908.0522.pdf |
1009.0763 | On the classification of quasihomogeneous singularities | [
"Claus Hertling",
"Ralf Kurbel"
] | 3 Sep 2010 (<a href="https://arxiv.org/abs/1009.0763v1">v1</a>), last revised 27 Apr 2016 (this version, v2) | 30 pages. In the 2nd version a misprint at the end of the proof of lemma 2.1 is corrected, the statements of lemma 2.4 and lemma 3.5 are corrected, and the table in section 5 is extended. The 2nd version coincides except for the new correction of lemma 3.5 with the published version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV) | https://doi.org/10.48550/arXiv.1009.0763 | The motivation for this paper are computer calculations of complete lists of weight systems of quasihomogeneous polynomials with isolated singularity at 0 up to rather large Milnor numbers. We review combinatorial characterizations of such weight systems for any number of variables. This leads to certain types and grap... | math-31-part-1.zip/1009.0763.pdf |
math/0601207 | The L-series of a cubic fourfold | [
"Klaus Hulek",
"Remke Kloosterman"
] | 10 Jan 2006 (<a href="https://arxiv.org/abs/math/0601207v1">v1</a>), last revised 2 Feb 2006 (this version, v2) | Modified some proofs | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Number Theory (math.NT) | https://doi.org/10.48550/arXiv.math/0601207 | We study the L-series of cubic fourfolds. Our main result is that, if X/C is a special cubic fourfold associated to some polarized K3 surface $S$, defined over a number field K such that S^[2](K) is not empty, then X has a model over K such that the L-series of the primitive cohomology of X/K can be expressed in the L-... | math-34-part-1.zip/math_0601207.pdf |
1304.1344 | Incidence and Combinatorial Properties of Linear Complexes | [
"Hans Havlicek",
"Corrado Zanella"
] | 4 Apr 2013 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Combinatorics (math.CO) | https://doi.org/10.48550/arXiv.1304.1344 | In this paper a generalisation of the notion of polarity is exhibited which allows to completely describe, in an incidence-geometric way, the linear complexes of $h$-subspaces. A generalised polarity is defined to be a partial map which maps $(h-1)$-subspaces to hyperplanes, satisfying suitable linearity and reciprocit... | math-31-part-2.zip/1304.1344.pdf | |
0802.2709 | Descent Systems for Bruhat Posets | [
"Lex E. Renner"
] | 19 Feb 2008 (<a href="https://arxiv.org/abs/0802.2709v1">v1</a>), last revised 5 Sep 2008 (this version, v3) | 23 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Group Theory (math.GR) | https://doi.org/10.48550/arXiv.0802.2709 | Let $(W,S)$ be a finite Weyl group and let $w\in W$. It is widely appreciated that the descent set D(w)=\{s\in S | l(ws)<l(w)\} determines a very large and important chapter in the study of Coxeter groups. In this paper we generalize some of those results to the situation of the Bruhat poset $W^J$ where $J\subseteq ... | math-31-part-1.zip/0802.2709.pdf |
1812.05648 | Euclidean distance degree of the multiview variety | [
"Laurentiu G. Maxim",
"Jose Israel Rodriguez",
"Botong Wang"
] | 13 Dec 2018 | Euclidean distance degree, multiview variety, triangulation problem, non-proper Morse theory, Euler-Poincare characteristic, local Euler obstruction | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.1812.05648 | The Euclidean distance degree of an algebraic variety is a well-studied topic in applied algebra and geometry. It has direct applications in geometric modeling, computer vision, and statistics. We use non-proper Morse theory to give a topological interpretation of the Euclidean distance degree of an affine variety in t... | math-32-part-2.zip/1812.05648.pdf |
2307.14393 | The cycle class of the supersingular locus of principally polarized abelian varieties | [
"Gerard van der Geer",
"Shushi Harashita"
] | 26 Jul 2023 (<a href="https://arxiv.org/abs/2307.14393v1">v1</a>), last revised 21 Jul 2025 (this version, v2) | 38 pages. To appear in Selecta Mathematica | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2307.14393 | We prove a formula for the cycle class of the supersingular locus in the Chow ring with rational coefficients of the moduli space of principally polarized abelian varieties in characteristic $p$. This formula determines this class as a monomial in the Chern classes of the Hodge bundle up to a factor that is a polynomia... | math-33-part-2.zip/2307.14393.pdf |
1412.2957 | The very good property for parabolic vector bundles over curves | [
"Alexander Soibelman"
] | 9 Dec 2014 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1412.2957 | The purpose of this note is to extend Beilinson and Drinfeld's "very good" property to moduli stacks of parabolic vector bundles on curves of genuses $g = 0$ and $g = 1$. Beilinson and Drinfeld show that for $g > 1$ a trivial parabolic structure is sufficient for the moduli stacks to be "very good... | math-31-part-2.zip/1412.2957.pdf | |
1612.07278 | The K-theory of versal flags and cohomological invariants of degree 3 | [
"Sanghoon Baek",
"Rostislav Devyatov",
"Kirill Zainoulline"
] | 21 Dec 2016 | 28pp | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1612.07278 | Let $G$ be a split semisimple linear algebraic group over a field and let $X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the Grothendieck ring $K_0(X)$ in terms of generators and relations in the case $G=G^{sc... | math-32-part-1.zip/1612.07278.pdf |
1912.02524 | $\mathbb{G}_a^3$-structures on del Pezzo fibrations | [
"Masaru Nagaoka"
] | 5 Dec 2019 (<a href="https://arxiv.org/abs/1912.02524v1">v1</a>), last revised 31 Jan 2020 (this version, v2) | 9 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1912.02524 | In this paper we prove that del Pezzo fibrations admit $\mathbb{G}_{a}^{3}$-structures if and only if they are $\mathbb{P}^2$-bundles over $\mathbb{P}^{1}$. | math-32-part-2.zip/1912.02524.pdf |
math/0604354 | Enlargements of Schemes | [
"Lars Bruenjes",
"Christian Serpe"
] | 16 Apr 2006 | 43 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Logic (math.LO) | https://doi.org/10.48550/arXiv.math/0604354 | In this article we use our constructions from "Enlargements of Categories" (Theory and Applications of Categories, 14:357-398) to lay down some foundations for the application of A. Robinson's nonstandard methods to modern Algebraic Geometry. The main motivation is the search for another tool to transfer re... | math-34-part-1.zip/math_0604354.pdf |
1911.00243 | Quantum $K$-theory of projective spaces and confluence of $q$-difference equations | [
"Alexis Roquefeuil"
] | 1 Nov 2019 (<a href="https://arxiv.org/abs/1911.00243v1">v1</a>), last revised 18 Jan 2022 (this version, v2) | 29 pages. Updated to add computations of monodromy. Comments are very welcomed | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Mathematical Physics (math-ph) | https://doi.org/10.48550/arXiv.1911.00243 | Givental's $K$-theoretical $J$-function can be used to reconstruct genus zero $K$-theoretical Gromov--Witten invariants. We view this function as a fundamental solution of a $q$-difference system. In the case of projective spaces, we show that we can use the confluence of $q$-difference systems to obtain the cohomo... | math-32-part-2.zip/1911.00243.pdf |
1704.05889 | Waldschmidt constants for Stanley-Reisner ideals of a class of graphs | [
"Tomasz Szemberg",
"Justyna Szpond"
] | 19 Apr 2017 | 7 pages, 2 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.1704.05889 | In the present note we study Waldschmidt constants of Stanley-Reisner ideals of a hypergraph and a graph with vertices forming a bipyramid over a planar n-gon. The case of the hypergraph has been studied by Bocci and Franci. We reprove their main result. The case of the graph is new. Interestingly, both cases provide s... | math-32-part-1.zip/1704.05889.pdf |
2508.14545 | Bekka's $(c)$-regularity condition and families of line singularities with constant Lê numbers | [
"Christophe Eyral",
"Öznur Turhan"
] | 20 Aug 2025 | 13 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2508.14545 | We show that the natural stratifications arising from certain deformation families of line singularities with constant Lê numbers satisfy Bekka's $(c)$-regularity condition. As a corollary, we obtain that these families are topologically equisingular. Similar results for families of isolated singularities were esta... | math-34-part-1.zip/2508.14545.pdf |
0810.4112 | Sums of residues on algebraic surfaces and application to coding theory | [
"Alain Couvreur"
] | 22 Oct 2008 | 31 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Information Theory (cs.IT) | https://doi.org/10.48550/arXiv.0810.4112 | In this paper, we study residues of differential 2-forms on a smooth algebraic surface over an arbitrary field and give several statements about sums of residues. Afterwards, using these results we construct algebraic-geometric codes which are an extension to surfaces of the well-known differential codes on curves. We ... | math-31-part-1.zip/0810.4112.pdf |
1109.4600 | Computer aided Unirationality Proofs of Moduli Spaces | [
"Frank-Olaf Schreyer"
] | 21 Sep 2011 | 28 pages, to appear in the Handbook of Moduli | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1109.4600 | We illustrate the use of the computer algebra system Macaulay2 for simplifications of classical unirationality proofs. We explicitly treat the moduli spaces of curves of genus g=10, 12 and 14. | math-31-part-1.zip/1109.4600.pdf |
2102.01799 | Non-torsion Brauer groups in positive characteristic | [
"Louis Esser"
] | 2 Feb 2021 (<a href="https://arxiv.org/abs/2102.01799v1">v1</a>), last revised 20 May 2022 (this version, v3) | 5 pages. Comments welcome! v3: final version, to appear in Proceedings of the American Mathematical Society | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2102.01799 | Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with non-torsion Brauer group. In contrast, we demonstrate that such examples cannot exist over... | math-33-part-1.zip/2102.01799.pdf |
alg-geom/9607021 | Embeddings of curves and surfaces | [
"F. Catanese",
"M. Franciosi",
"K. Hulek",
"M. Reid"
] | 22 Jul 1996 | LaTeX2e with packages: amstex, amssymb, theorem. 32 pp | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.alg-geom/9607021 | We prove a general embedding theorem for Cohen--Macaulay curves (possibly nonreduced), and deduce a cheap proof of the standard results on pluricanonical embeddings of surfaces, assuming vanishing H^1(2K_X)=0. | small_categories-00.zip/alg-geom_9607021.pdf |
math/9904076 | Toroidal varieties and the weak Factorization Theorem | [
"Jaroslaw Wlodarczyk"
] | 15 Apr 1999 (<a href="https://arxiv.org/abs/math/9904076v1">v1</a>), last revised 25 Jul 2002 (this version, v5) | 69 pages, a revised version with conceptual simplifications. The present version is self-contained and it does not rely on weak factorization theorem for toric varieties | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Complex Variables (math.CV); Differential Geometry (math.DG) | https://doi.org/10.48550/arXiv.math/9904076 | The main goal of the present paper is two-fold. First we extend the theory of toroidal embeddings introduced by Kempf, Knudsen, Mumford and Saint-Donat to the class of toroidal varieties with stratifications (which is the main body of the paper). Second we give a proof of the following weak factorization theorem as an ... | math-34-part-2.zip/math_9904076.pdf |
0707.2441 | A Galois-theoretic approach to Kanev's correspondence | [
"H. Lange",
"A. Rojas"
] | 17 Jul 2007 | 15 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.0707.2441 | Let $G$ be a finite group, $\Lambda$ an absolutely irreducible $\Z[G]$-module and $w$ a weight of $\Lambda$. <br>To any Galois covering with group $G$ we associate two correspondences, the Schur and the Kanev correspondence. <br>We work out their relation and compute their invariants. <br>Using this, we give some new e... | math-30-part-2.zip/0707.2441.pdf |
math/0105176 | Numerical characterization of the Kähler cone of a compact Kähler manifold | [
"Jean-Pierre Demailly",
"Mihai Paun"
] | 22 May 2001 (<a href="https://arxiv.org/abs/math/0105176v1">v1</a>), last revised 24 Sep 2001 (this version, v2) | 27 pages, Plain-TeX (new version: section 5 on deformations added) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0105176 | The goal of this work is give a precise numerical description of the Kähler cone of a compact Kähler manifold. Our main result states that the Kähler cone depends only on the intersection form of the cohomology ring, the Hodge structure and the homology classes of analytic cycles: if $X$ is a compact Kähler manifold, t... | math-34-part-1.zip/math_0105176.pdf |
2404.15412 | The log-open correspondence for two-component Looijenga pairs | [
"Yannik Schuler"
] | 23 Apr 2024 (<a href="https://arxiv.org/abs/2404.15412v1">v1</a>), last revised 6 May 2025 (this version, v2) | 27 pages. Typos fixed. Accepted version | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2404.15412 | A two-component Looijenga pair is a rational smooth projective surface with an anticanonical divisor consisting of two transversally intersecting curves. We establish an all-genus correspondence between the logarithmic Gromov-Witten theory of a two-component Looijenga pair and open Gromov-Witten theory of a toric Calab... | math-33-part-2.zip/2404.15412.pdf |
2307.08830 | Extensions of tautological rings and motivic structures in the cohomology of $\overline{\mathcal{M}}_{g,n}$ | [
"Samir Canning",
"Hannah Larson",
"Sam Payne"
] | 17 Jul 2023 (<a href="https://arxiv.org/abs/2307.08830v1">v1</a>), last revised 25 Oct 2024 (this version, v3) | v3: 33 pages. Minor changes. Final version to appear in Forum Math. Pi | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2307.08830 | We study collections of subrings of $H^*(\overline{\mathcal{M}}_{g,n})$ that are closed under the tautological operations that map cohomology classes on moduli spaces of smaller dimension to those on moduli spaces of larger dimension and contain the tautological subrings. Such extensions of tautological rings are well-... | math-33-part-2.zip/2307.08830.pdf |
2405.07092 | Belyi Function Decompositions for The Icosahedron of Genus 4 | [
"Natalia Amburg",
"Mariia Kovaleva"
] | 11 May 2024 | 22 pages, 15 figures | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2405.07092 | The icosahedron $I_4$ of genus 4 is a dessin d'enfant embedded in Bring's curve $\mathcal{B}$. The dessin $I_4$ is related in some sense to a regular icosahedron $I_0$ embedded in the complex Riemann sphere. In particular, decompositions of Belyi functions $\beta_{I_0}: \mathbb{CP}^1 \rightarrow \mathbb{CP}^1$ ... | math-33-part-2.zip/2405.07092.pdf |
math/0110102 | ACM bundles on a general quintic threefold | [
"L.Chiantini",
"C.Madonna"
] | 9 Oct 2001 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0110102 | We give a partial positive answer to a conjecture of Tyurin (\cite {Tyu}). Indeed we prove that on a general quintic hypersurface of $\Pj^4$ every arithmetically Cohen--Macaulay rank 2 vector bundle is infinitesimally rigid. | math-34-part-1.zip/math_0110102.pdf | |
2306.04183 | Downgrading of a T-variety | [
"Pavankumar Dighe",
"Vivek Mohan Mallick"
] | 7 Jun 2023 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2306.04183 | For an affine $T$-variety $X$ with the action of a torus $T$, this paper provides a combinatorial description of $X$ with respect to the action of a subtorus $T' \subset T$ in terms of a $T/T'$-invariant pp-divisor. We also describe the corresponding GIT fan. | math-33-part-2.zip/2306.04183.pdf | |
2507.02317 | Birational equivalence of exponential matrices | [
"Ryuji Tanimoto"
] | 3 Jul 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.2507.02317 | Let $k$ be an algebraically closed field of characteristic $p \geq 0$ and let $\mathbb{G}_a$ denote the additive group of $k$. We give one-to-one correspondences between exponentional matrices and various objects, and in particular give a one-to-one correspondence between exponential matrices of size $n$-by-$n$ and $\m... | math-34-part-1.zip/2507.02317.pdf | |
2509.15831 | Atoms meet symbols | [
"Leonardo F. Cavenaghi",
"Ludmil Katzarkov",
"Maxim Kontsevich"
] | 19 Sep 2025 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Differential Geometry (math.DG); Symplectic Geometry (math.SG) | https://doi.org/10.48550/arXiv.2509.15831 | This paper introduces a novel framework for constructing invariants in $G$-equivariant birational geometry by unifying two recent approaches: the \emph{theory of atoms} recently developed by Katzarkov, Kontsevich, Pantev, and Yu, and the theory of \emph{modular symbols} due to Kontsevich, Tschinkel, and Pestun. <br>We ... | math-34-part-1.zip/2509.15831.pdf | |
2112.12401 | On the Calogero-Moser space associated with dihedral groups II. The equal parameter case | [
"Cédric Bonnafé"
] | 23 Dec 2021 (<a href="https://arxiv.org/abs/2112.12401v1">v1</a>), last revised 6 Feb 2022 (this version, v2) | 21 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Representation Theory (math.RT) | https://doi.org/10.48550/arXiv.2112.12401 | We continue the study of Calogero-Moser spaces associated with dihedral groups by investigating in more details the equal parameter case: we obtain explicit equations, some informations about the Poisson bracket, the structure of the Lie algebra associated with the cuspidal point and the action of $SL_2(\mathbb{C})$. | math-33-part-1.zip/2112.12401.pdf |
2407.14832 | On a fibre bundle version of the Caporaso-Harris formula | [
"Indranil Biswas",
"Apratim Choudhury",
"Nilkantha Das",
"Ritwik Mukherjee"
] | 20 Jul 2024 | 38 pages, 7 figures. Comments are welcome | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2407.14832 | The Caporaso-Harris formula gives a recursive algorithm to enumerate delta nodal degree d curves in P^2. The recursion is obtained in terms of curves of lower degree that are tangent to a given divisor. This paper presents two generalizations of this method. The first result is on enumeration of one cuspidal curves on ... | math-33-part-2.zip/2407.14832.pdf |
alg-geom/9310007 | Initial ideals, Veronese subrings, and rates of algebras | [
"David Eisenbud",
"Alyson Reeves",
"Burt Totaro"
] | 11 Oct 1993 | 24 pages, latex file | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.alg-geom/9310007 | We show that high Veronese subrings of any commutative graded ring have a Grobner basis with all relations of degree 2. (The d-th Veronese subring of a ring A_0 + A_1 + A_2 + ... is the ring A_0 + A_d + A_{2d} + ...; ``high'' means we take d sufficiently large, say at least half the regularity of the ideal defi... | small_categories-00.zip/alg-geom_9310007.pdf |
2301.11232 | The nilpotent quotients of normal quasi-projective varieties with proper quasi-Albanese map | [
"Rodolfo Aguilar Aguilar",
"Frédéric Campana"
] | 26 Jan 2023 (<a href="https://arxiv.org/abs/2301.11232v1">v1</a>), last revised 19 Apr 2023 (this version, v4) | Acknowledgements section included, bibliography and references updated, two extra remarks | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2301.11232 | We show that if $X$ is a normal complex quasi-projective variety, the quasi-Albanese map of which is proper, then the torsionfree nilpotent quotients of $\pi_1(X)$ are, up to a controlled finite index, the same ones as those of the normalisation of its quasi-Albanese image. When $X$ is quasi-Kähler smooth, we get the s... | math-33-part-1.zip/2301.11232.pdf |
1509.08749 | Covariant algebra of the binary nonic and the binary decimic | [
"Reynald Lercier",
"Marc Olive"
] | 29 Sep 2015 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1509.08749 | We give a minimal system of 476 generators (resp. 510 generators) for the algebra of SL(2,C)-covariant polynomials on binary forms of degree 9 (resp. degree 10). These results were only known as conjectures so far. The computations rely on Gordan's algorithm, and some new improvements. | math-32-part-1.zip/1509.08749.pdf | |
1202.0542 | Geometric structures on finite- and infinite-dimensional Grassmannians | [
"Andrea Blunck",
"Hans Havlicek"
] | 31 Jan 2012 (<a href="https://arxiv.org/abs/1202.0542v1">v1</a>), last revised 14 Mar 2012 (this version, v3) | Correction of two typos | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1202.0542 | In this paper, we study the Grassmannian of n-dimensional subspaces of a 2n-dimensional vector space and its infinite-dimensional analogues. Such a Grassmannian can be endowed with two binary relations (adjacent and distant), with pencils (lines of the Grassmann space) and with so-called Z-reguli. We analyse the interd... | math-31-part-2.zip/1202.0542.pdf |
math/0608008 | On isomorphisms of factorial domains and the Jacobian conjecture in any characteristic | [
"Kossivi Adjamagbo"
] | 1 Aug 2006 | This paper presents the first reformulations in positive characteristic of the Jacobian conjecture in zero characteristic, thanks to methods of model theory. Such reformulations are usefull for the proof of the equivalence of Jacobian, Dixmier and Poisson conjectures in any characteristic, as explained in another ArXiv... | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Commutative Algebra (math.AC) | https://doi.org/10.48550/arXiv.math/0608008 | The main theorem (2.2) consists in two characterizations of isomorphisms of factorial domains in terms of prime or primary rings elements, and unramified, flat or weakly injective affine schemes morphisms. In order to apply this theorem to the famous Jacobian Conjecture, we first introduce its different versions in any... | math-34-part-1.zip/math_0608008.pdf |
2104.07074 | Generic Vanishing, 1-forms, and Topology of Albanese Maps | [
"Yajnaseni Dutta",
"Feng Hao",
"Yongqiang Liu"
] | 14 Apr 2021 (<a href="https://arxiv.org/abs/2104.07074v1">v1</a>), last revised 4 Jan 2024 (this version, v4) | Final version to appear in Math Zeitschrift: rewrote the introduction and abstract from a slightly different perspective. Shortened exposition, with some deleted proofs as per referee's comments. Added a special case of the main theorem in positive characteristics (Proposition 3.7). 18 pages, comments are very welc... | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Algebraic Topology (math.AT) | https://doi.org/10.48550/arXiv.2104.07074 | Given a bounded constructible complex of sheaves $\mathcal{F}$ on a complex Abelian variety, we prove an equality relating the cohomology jump loci of $\mathcal{F}$ and its singular support. As an application, we identify two subsets of the set of holomorphic 1-forms with zeros on a complex smooth projective irregular ... | math-33-part-1.zip/2104.07074.pdf |
math/0410444 | Braid Monodromy Computation of Real Singular Curves | [
"S. Kaplan",
"E. Liberman",
"M. Teicher"
] | 20 Oct 2004 | 46 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Geometric Topology (math.GT) | https://doi.org/10.48550/arXiv.math/0410444 | We generalize the Moishezon Teicher algorithm that was suggested for the computation of the braid monodromy of an almost real curve. The new algorithm suits a larger family of curves, and enables the computation of braid monodromy not only of caspidal curves, but of general algebraic curves, with some non simple singul... | math-34-part-1.zip/math_0410444.pdf |
1604.08662 | Triangulated endofunctors of the derived category of coherent sheaves which do not admit DG liftings | [
"Vadim Vologodsky"
] | 29 Apr 2016 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); K-Theory and Homology (math.KT) | https://doi.org/10.48550/arXiv.1604.08662 | Recently, Rizzardo and Van den Bergh constructed an example of a triangulated functor between the derived categories of coherent sheaves on smooth projective varieties over a field $k$ of characteristic $0$ which is not of the Fourier-Mukai type. The purpose of this note is to show that if $char \, k =p$ then there are... | math-32-part-1.zip/1604.08662.pdf | |
math/0301251 | Seshadri Constants and the geometry of surfaces | [
"Michael Nakamaye"
] | 22 Jan 2003 | 10 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0301251 | We examine how the Seshadri constant of an ample line bundle at a very general point of an algebraic surface can carry important global geometric information about the surface. In particular, we obtain a numerical criterion for when a surface admits a dominant map to an algebraic curve. | math-34-part-1.zip/math_0301251.pdf |
2008.06159 | Asymptotic shifting numbers in triangulated categories | [
"Yu-Wei Fan",
"Simion Filip"
] | 14 Aug 2020 (<a href="https://arxiv.org/abs/2008.06159v1">v1</a>), last revised 1 Sep 2020 (this version, v2) | 43 pages, 1 figure | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Category Theory (math.CT); Dynamical Systems (math.DS) | https://doi.org/10.48550/arXiv.2008.06159 | We introduce invariants, called shifting numbers, that measure the asymptotic amount by which an autoequivalence of a triangulated category translates inside the category. The invariants are analogous to Poincare translation numbers that are widely used in dynamical systems. We additionally establish that in some examp... | math-33-part-1.zip/2008.06159.pdf |
math/0001113 | A remark on the Chisini conjecture | [
"Stefan Nemirovski"
] | 20 Jan 2000 | 5 pages, LaTeX2e | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.math/0001113 | The Chisini conjecture asserts that a generic ramified covering over the complex projective plane of degree at least 5 is uniquely determined by its branch curve. We prove this for degree at least 12 using the work of Kulikov (math-AG/9803144). | math-34-part-1.zip/math_0001113.pdf |
1810.03434 | On stability conditions for the quintic threefold | [
"Chunyi Li"
] | 8 Oct 2018 (<a href="https://arxiv.org/abs/1810.03434v1">v1</a>), last revised 29 Apr 2019 (this version, v2) | pre-journal version, 32 pages, 7 figures, comments are very welcome! | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1810.03434 | We study the Clifford type inequality for a particular type of curves $C_{2,2,5}$, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previ... | math-32-part-2.zip/1810.03434.pdf |
alg-geom/9604018 | Eisenstein series and quantum affine algebras | [
"M.M. Kapranov"
] | 26 Apr 1996 (<a href="https://arxiv.org/abs/alg-geom/9604018v1">v1</a>), last revised 23 Nov 1996 (this version, v2) | plain TEX, 70 pages, no figures; misprints in some formulas are corrected and new references to relevant work added | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Quantum Algebra (math.QA) | https://doi.org/10.48550/arXiv.alg-geom/9604018 | Let X be a smooth projectibe curve over a finite field. We consider the Hall algebra H whose basis is formed by isomorphism classes of coherent sheaves on X and whose typical structure constant is the number of subsheaves in a given sheaf belonging to a given isomorphism class and with given isomorphism class of quotie... | small_categories-00.zip/alg-geom_9604018.pdf |
1802.06333 | Explicit equations of a fake projective plane | [
"Lev A. Borisov",
"JongHae Keum"
] | 18 Feb 2018 (<a href="https://arxiv.org/abs/1802.06333v1">v1</a>), last revised 16 Apr 2019 (this version, v3) | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1802.06333 | Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to those of the usual projective plane. They come in complex conjugate pairs and have been classified as quotients of the two-dimensional ball by explicitly written arithmetic subgroups. In this paper we find equations of a proj... | math-32-part-2.zip/1802.06333.pdf | |
1711.10259 | A Saito criterion for holonomic divisors | [
"Raul Epure",
"Mathias Schulze"
] | 28 Nov 2017 (<a href="https://arxiv.org/abs/1711.10259v1">v1</a>), last revised 11 Sep 2018 (this version, v3) | 8 pages | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1711.10259 | We show that a holonomic divisor is free if and only if applying all logarithmic derivations to a generic function with isolated critical point yields a complete intersection Artin algebra. | math-32-part-2.zip/1711.10259.pdf |
1312.6358 | Which abelian tensor categories are geometric? | [
"Daniel Schäppi"
] | 22 Dec 2013 (<a href="https://arxiv.org/abs/1312.6358v1">v1</a>), last revised 2 May 2014 (this version, v2) | 42 pages. Improved exposition; version accepted for publication in Crelle's Journal | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG); Category Theory (math.CT) | https://doi.org/10.48550/arXiv.1312.6358 | For a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a characterization of tensor categories in the image of this embedding. <br>However, ... | math-31-part-2.zip/1312.6358.pdf |
2405.04701 | The Enumerative Geometry and Arithmetic of Banana Nano-Manifolds | [
"Jim Bryan",
"Stephen Pietromonaco"
] | 7 May 2024 | Appendix with Mike Roth | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.2405.04701 | A banana manifold is a Calabi-Yau threefold fibered by Abelian surfaces whose singular fibers contain banana configurations: three rational curves meeting each other in two points. A nano-manifold is a Calabi-Yau threefold $X$ with very small Hodge numbers: $h^{1,1}(X)+h^{2,1}(X)\leq 6$. We construct four rigid banana ... | math-33-part-2.zip/2405.04701.pdf |
1810.11848 | Triangle varieties and surface decomposition of hyper-Kähler manifolds | [
"Claire Voisin"
] | 28 Oct 2018 | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1810.11848 | We introduce and study the notion of "surface decomposable" variety, and discuss the possibility that any projective hyper-Kähler manifold is surface decomposable, which would produce new evidence for Beauville's weak splitting conjecture. We show that surface decomposability relates to the Beauville-Fujiki... | math-32-part-2.zip/1810.11848.pdf | |
1402.6051 | Integral Hodge classes on fourfolds fiberd by quadric bundles | [
"Zhiyuan Li",
"Zhiyu Tian"
] | 25 Feb 2014 (<a href="https://arxiv.org/abs/1402.6051v1">v1</a>), last revised 31 Oct 2014 (this version, v3) | As we think that our geometric approach might still be interesting, we make it available. There will be a future work related to this paper. Some typos have been fixed | Algebraic Geometry (math.AG) | Algebraic Geometry (math.AG) | https://doi.org/10.48550/arXiv.1402.6051 | We discuss the space of sections and certain bisections on a quadric surfaces bundle $X$ over a smooth curve. The Abel-Jacobi from these spaces to the intermediate Jacobian will be shown to be dominant with rationally connected fibers. As an application, we prove that the integral Hodge conjecture holds for degree four... | math-31-part-2.zip/1402.6051.pdf |
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