## Algebraic Geometry Seminar

Aaron Landesman

Harvard University

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 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.

Monday September 23, 2024 at 3:00 PM in 636 SEO