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

Abstract: In this work, we introduce the moduli stack $\widetilde{\mathcal{M}}_{g,n}^r$ 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 $\widetilde{\mathcal{M}}_3^7$. All the Chow rings are assumed to be with coefficients in $\mathbb{Z}[1/6]$.