Euler characteristics of moduli spaces of curves

Abstract

Let ${\mathcal{M}}_g^n$ be the moduli space of $n$-pointed Riemann surfaces of genus $g$. Denote by ${\overline{\mathcal{M}}}_g^n$ the Deligne-Mumford compactification of ${\mathcal{M}}_g^n$. In the present paper, we calculate the orbifold and the ordinary Euler characteristic of ${\overline{\mathcal{M}}}_g^n$ for any $g$ and $n$ such that $n>2-2g$.