#### Vol. 9, No. 2, 2015

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The Picard rank conjecture for the Hurwitz spaces of degree up to five

### Anand Deopurkar and Anand Patel

Vol. 9 (2015), No. 2, 459–492
##### Abstract

We prove that the rational Picard group of the simple Hurwitz space ${\mathsc{ℋ}}_{d,g}$ is trivial for $d$ up to five. We also relate the rational Picard groups of the Hurwitz spaces to the rational Picard groups of the Severi varieties of nodal curves on Hirzebruch surfaces.

##### Keywords
Hurwitz space, Picard group
Primary: 14H10
Secondary: 14C22