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

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

2007-07-18

arxiv.org/abs/0707.2662v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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 $\mathcal{M}_{2,n}$.

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