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