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

TL;DR

This paper proves that the Chow ring of the Hurwitz space for degree three covers of the projective line is tautological and computes related Picard groups, advancing understanding of these moduli spaces.

Contribution

It establishes the tautological nature of the Chow ring for degree three Hurwitz spaces and calculates associated Picard groups, providing new structural insights.

Findings

Chow ring of the Hurwitz space is tautological

Computed rational Picard groups of auxiliary spaces

Enhanced understanding of moduli spaces of degree three covers

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.