The integral Picard groups of low-degree Hurwitz spaces

Abstract

We compute the Picard groups with integral coefficients of the Hurwitz stacks parametrizing degree $4$ and $5$ covers of ${\mathbb{P}}^1$. As a consequence, we also determine the integral Picard groups of the Hurwitz stacks parametrizing simply branched covers. For simple branching, the Picard groups are finite, with order depending on the genus.

21 pages, split off from arXiv:2103.09902v1 because of length, added Corollary 1.3