Algebraic Geometry Seminar

Title: Euler characteristics of strata of k-differentials

Abstract: Strata of k-differentials are natural subvarieties of moduli spaces of curves obtained by prescribing the orders of zeros and poles of a k-differential. In this talk, I will present an explicit formula for their orbifold Euler characteristics, generalising the classical Harer–Zagier formula for the moduli space of curves. As a consequence, we show that these Euler characteristics depend polynomially on the orders of the zeros and poles. I will then present an intersection-theoretic expression in terms of tautological integrals over double ramification cycles, as well as a recursion that determines the Euler characteristics from genus zero. Based on joint work with M. Costantini, M. Möller, A. Sauvaget, and J. Schmitt.