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 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