Papers › Tautological classes on low-degree Hurwitz spaces
Tautological classes on low-degree Hurwitz spaces
Samir Canning, Hannah Larson
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Let ℋ_(k,g) be the Hurwitz stack parametrizing degree k, genus g covers of ℙ¹. We define the tautological ring of 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 ≤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 ≤5.
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