Michele Pernice: A_r -stable curves and the (almost) integral Chow ring of M3bar
Time: Wed 2023-01-18 13.15
Location: Albano, Cramér room
Participating: Michele Pernice, KTH
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 \(\overline{\mathcal{M}}_3\).