Stable cuspidal curves and the integral Chow ring of ${\overline{\mathcal{M}}}_{2,1}$

Abstract

In this paper we introduce the moduli stack ${\tilde{\mathcal{M}}}_{g,n}$ of $n$-marked stable at most cuspidal curves of genus $g$ and we use it to determine the integral Chow ring of ${\overline{\mathcal{M}}}_{2,1}$. Along the way, we also determine the integral Chow ring of ${\overline{\mathcal{M}}}_{1,2}$.

47 pages, comments welcome! V2: some mistakes corrected, some new figures added. To appear on Geometry & Topology