On the Chow ring of the Hurwitz space of degree three covers of ${\mathbf{P}}^1$

Abstract

We determine that the Chow ring (with $\mathbf{Q}$-coefficients) of the Hurwitz space parametrizing degree three covers of ${\mathbf{P}}^1$ is tautological. We also compute the rational Picard groups of auxiliary spaces of degree three maps with special marked points.

18 pages. The portion in version 1 determining the exact Chow ring had a major flaw, as was kindly pointed out to us by Hannah Larson. We thank Hannah Larson and Samir Canning for going much further in their work on Chow rings of low degree Hurwitz spaces

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