Algebraic Geometry in String Theory Seminar

Speaker: Aaron Landesman, MIT

Title: Geometric local systems on very general curves

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 amore 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.