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arXiv · 2207.10873

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

Samir Canning·Hannah Larson
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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 $n \leq 2g+6$. 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 $n \leq 2g+8$ to show $\mathcal{H}_{g,n}$ is rational for $n \leq 3g+5$.

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Samir Canning, Hannah Larson. 2022-07-22. The rational Chow rings of moduli spaces of hyperelliptic curves with marked points. https://arxiv.org/abs/2207.10873

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