Euler Characteristics of Moduli Spaces of Curves

Abstract

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