Aaron Landesman : Geometric local systems on very general curves

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Sept. 23, 2024, 3 p.m.

In

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Abstract

What is the smallest genus h of a non-isotrivial curve over the generic genus g curve? In joint work with Daniel Litt, we show h is more than $\sqrt{g}$ by proving a more general result about variations of Hodge structure on sufficiently general curves. As a consequence, we show that local systems on a sufficiently general curve of geometric origin are not Zariski dense in the character variety parameterizing such local systems. This gives counterexamples to conjectures of Esnault-Kerz and Budur-Wang.