Samuel Grushevsky : Ends of strata of differentials

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

At

March 31, 2025, 3 p.m.

In

712 SEO

Abstract

A stratum of differentials is the moduli space of curves together with a meromorphic form with prescribed multiplicities of zeroes and poles. The strata are phase spaces of an action of SL(2,R) and thus the central object of study in Teichmueller dynamics. On the other hand, they give natural high codimension subvarieties of the moduli of curves with marked points. The strata are non-compact, and we determine the number of their ends, and discuss a viewpoint towards further homology computations. This uses an algebraic compactification of the strata. Based on a joint work with Ben Dozier.