On the $S_n$-equivariant Euler characteristic of moduli spaces of hyperelliptic curves

The generating function for $S_n$-equivariant Euler characteristics of moduli spaces of pointed hyperelliptic curves for any genus $g\ge 2$ is calculated. This answer generalizes the known ones for genera 2 and 3 and the answers obtained by J. Bergstr$\ddot{o}$m for any genus and $n\le 7$ points.

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Published 1 January 2009