非常一般的曲线和同构上的几何局部系统

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2023-11-03 DOI:10.1090/jams/1038

Aaron Landesman, Daniel Litt

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引用次数: 0

摘要

证明了在适当的一般n n点g属曲线上的几何原点非等平凡局部系统的最小秩至少为2g +1 2\sqrt {g+1}。我们用这个结果来解决Esnault-Kerz和Budur-Wang的猜想。主要输入是分析等单调变形下平面矢量束的稳定性，这也回答了Biswas, Heu和Hurtubise的问题。

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Geometric local systems on very general curves and isomonodromy

We show that the minimum rank of a non-isotrivial local system of geometric origin on a suitably general n n -pointed curve of genus g g is at least 2 g + 1 2\sqrt {g+1} . We apply this result to resolve conjectures of Esnault-Kerz and Budur-Wang. The main input is an analysis of stability properties of flat vector bundles under isomonodromic deformations, which additionally answers questions of Biswas, Heu, and Hurtubise.

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来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.