$A_r$-stable curves and the Chow ring of ${\overline{\mathcal{M}}}_3$

Abstract

In this work, we introduce the moduli stack ${\tilde{\mathcal{M}}}_{g,n}^r$ of $n$-pointed, $A_r$-stable curves of genus $g$ and use it to compute the Chow ring of ${\overline{\mathcal{M}}}_3$. As a byproduct, we also compute the Chow ring of ${\tilde{\mathcal{M}}}_3^7$. All the Chow rings are assumed to be with coefficients in $\mathbb{Z}[1/6]$.

arXiv commentThis is the PhD thesis of the author; 129 pages; comments are very welcome