The rational Chow rings of moduli spaces of hyperelliptic curves with marked points

Abstract

We determine the rational Chow ring of the moduli space ${\mathcal{H}}_{g,n}$ of $n$-pointed smooth hyperelliptic curves of genus $g$ when $n\le 2g+6$. We also show that the Chow ring of the partial compactification ${\mathcal{I}}_{g,n}$, parametrizing $n$-pointed irreducible nodal hyperelliptic curves, is generated by tautological divisors. Along the way, we improve Casnati's result that ${\mathcal{H}}_{g,n}$ is rational for $n\le 2g+8$ to show ${\mathcal{H}}_{g,n}$ is rational for $n\le 3g+5$.

28 pages, comments welcome!