Tautological classes on low-degree Hurwitz spaces

Samir Canning; Hannah Larson

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arXiv · 2103.09902

Tautological classes on low-degree Hurwitz spaces

Samir Canning·Hannah Larson

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Abstract

Let $\mathcal{H}_{k,g}$ be the Hurwitz stack parametrizing degree $k$, genus $g$ covers of $\mathbb{P}^1$. We define the tautological ring of $\mathcal{H}_{k,g}$ and we show that all Chow classes, except possibly those supported on the locus of "factoring covers," are tautological up to codimension roughly $g/k$ when $k \leq 5$. The set-up developed here is also used in our subsequent work, wherein we prove new results about the structure of the Chow ring for $k \leq 5$.

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Samir Canning, Hannah Larson. 2021-03-17. Tautological classes on low-degree Hurwitz spaces. https://arxiv.org/abs/2103.09902

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