On the S_n-equivariant Euler characteristic of M_{2,n}

Abstract

The Getzler's formula relates the S_n-equivariant Hodge-Deligne polynomial of the space of ordered tuples of distinct points on a given variety X with the Hodge-Deligne polynomial of X. We obtain the analogue of this formula for the case when X has a nontrivial automorphism group. Collecting together all strata of ${\mathcal{M}}_2$ with different automorphism groups, we derive a formula for the S_n-equivariant Euler characteristic of ${\mathcal{M}}_{2,n}$.

14 pages

References in corpus (1)

• Rational cohomology of the moduli space of genus 4 curves