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