Torelli theorem for moduli stacks of vector bundles and principal G-bundles

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-10-29 DOI:10.1016/j.geomphys.2024.105350

David Alfaya , Indranil Biswas , Tomás L. Gómez , Swarnava Mukhopadhyay

引用次数: 0

Abstract

Given any irreducible smooth complex projective curve X, of genus at least 2, consider the moduli stack of vector bundles on X of fixed rank and determinant. It is proved that the isomorphism class of the stack uniquely determines the isomorphism class of the curve X and the rank of the vector bundles. The case of trivial determinant, rank 2 and genus 2 is specially interesting: the curve can be recovered from the moduli stack, but not from the moduli space (since this moduli space is

P^{3}

thus independently of the curve).

We also prove a Torelli theorem for moduli stacks of principal G-bundles on a curve of genus at least 3, where G is any non-abelian reductive group.

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向量束和主 G 束模堆的托勒里定理

给定任何不可还原的光滑复射曲线 X（其属至少为 2），考虑 X 上具有固定秩和行列式的向量束的模堆栈。证明了堆栈的同构类唯一地决定了曲线 X 的同构类和向量束的秩。三阶行列式、秩 2 和属 2 的情况特别有趣：曲线可以从模数堆栈中恢复，但不能从模数空间中恢复（因为这个模数空间是 P3，因此与曲线无关）。我们还证明了关于至少属 3 的曲线上主 G 束的模数堆栈的托勒里定理，其中 G 是任何非阿贝尔还原群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity