Geometric local systems on very general curves

CMSA EVENTS: CMSA ALGEBRAIC GEOMETRY IN STRING THEORY SEMINAR

When: April 18, 2024
10:15 am - 11:15 am
Where: CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138, United States
Speaker: Aaron Landesman - MIT
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.