Michele Pernice: A_r -stable curves and the (almost) integral Chow ring of M3bar

Abstract

The rational Chow ring of the moduli stack of stable curves is as interesting as it is hard to compute. In this talk, we will present a strategy for computing such invariant for the genus 3 case, in fact obtaining the Chow ring of \(\overline{\mathcal{M}}_3\) with \(\mathbb{Z}[1/6]\)-coefficients. This extends the result of Faber which describes the rational Chow ring of \(\overline{\mathcal{M}}_3\). To do so, we introduce a bigger moduli stack of curves (allowing worse-than-nodal singularities to appear), compute its Chow ring and then use localization sequence to finally get the Chow ring of \(\overline{\mathcal{M}}_3\).