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

Abstract

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