The integral Picard groups of low-degree Hurwitz spaces

Samir Canning; Hannah Larson

The integral Picard groups of low-degree Hurwitz spaces

Algebraic Geometry 2021-10-29 v1

Authors: Samir Canning , Hannah Larson

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.

Keywords

hurwitz stacks picard groups integral coefficients branched covers genus

Cite

@article{arxiv.2110.14727,
  title  = {The integral Picard groups of low-degree Hurwitz spaces},
  author = {Samir Canning and Hannah Larson},
  journal= {arXiv preprint arXiv:2110.14727},
  year   = {2021}
}

Comments

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

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