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

Deopurkar, Anand; Patel, Anand

doi:10.2140/ant.2015.9.459

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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

DOI: 10.2140/ant.2015.9.459

Abstract

We prove that the rational Picard group of the simple Hurwitz space $ℋ_{d, g}$ 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

Mathematical Subject Classification 2010

Primary: 14H10

Secondary: 14C22

Milestones

Received: 27 July 2014

Revised: 4 November 2014

Accepted: 11 December 2014

Published: 5 March 2015

Authors

Anand Deopurkar
Department of Mathematics Columbia University 2990 Broadway New York, NY 10027 United States

Anand Patel
Mathematics Department Boston College Carney Hall Chestnut Hill, MA 02467 United States

Vol. 9, No. 2, 2015