Abstract

The study of intersection theory on moduli spaces and stacks has a rich history, beginning with Mumford’s seminal 1983 paper, where he introduced the Chow ring with rational coefficients for the moduli space of smooth pointed curves of a given genus and its Deligne–Mumford compactification. This framework was later extended by Vistoli to Deligne–Mumford stacks, by Edidin and Graham to quotient stacks, and more generally by Kresch to both integral and rational coefficients. Since then, extensive research has been devoted to computing the intersection theory of various moduli stacks.

In this talk, we will focus on the integral version of Chow rings, which is generally less well understood. I will first review some known results in this direction. I will then outline the computation of the integral Chow ring of the moduli stack of hyperelliptic Prym curves, which are étale double covers of hyperelliptic curves—a result that Alessio Cela and I recently obtained. In the case of genus two, our results recover a previous computation by Cela and Lopez.