Compactification of moduli of holomorphic differentials.

https://bbb.mpim-bonn.mpg.de/b/gae-a7y-hhd

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 various 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.