25 nov 2015 -- 14:30
Aula di Consiglio, Dip. Matematica, Università "La Sapienza", Roma
Abstract.
The moduli space of holomorphic differentials (with prescribed zeros and poles) on nonsingular curves is not compact since the curve may degenerate. I will discuss a compactification of these strata in the moduli space of Deligne-Mumford stable pointed curves, which includes the space of canonical divisors as an open subset. The theory leads to geometric-combinatorial constraints on the closures of the strata of holomorphic differentials and as a consequence, one can determine the cohomology classes of the strata. This is joint work with Rahul Pandharipande.