Geometric local systems on very general curves and isomonodromy

2022/01/31 by Aaron Landesman, Daniel Litt, Landesman, Aaron +1
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2202.00039

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√(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 deformation, which additionally answers questions of Biswas, Heu, and Hurtubise.

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