Geometric local systems on very general curves and isomonodromy

Landesman, Aaron; Litt, Daniel

doi:10.1090/jams/1038

Geometric local systems on very general curves and isomonodromy
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by Aaron Landesman and Daniel Litt

J. Amer. Math. Soc. 37 (2024), 683-729

DOI: https://doi.org/10.1090/jams/1038

Published electronically: November 3, 2023

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Abstract:

We show that the minimum rank of a non-isotrivial local system of geometric origin on a suitably general $n$-pointed curve of genus $g$ is at least $2\sqrt {g+1}$. 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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