Vol. 9, No. 4, 2016

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Jacobian varieties of Hurwitz curves with automorphism group $\mathrm{PSL}(2,q)$

Allison Fischer, Mouchen Liu and Jennifer Paulhus

Vol. 9 (2016), No. 4, 639–655
Abstract

The size of the automorphism group of a compact Riemann surface of genus g > 1 is bounded by 84(g 1). Curves with automorphism group of size equal to this bound are called Hurwitz curves. In many cases the automorphism group of these curves is the projective special linear group PSL(2,q). We present a decomposition of the Jacobian varieties for all curves of this type and prove that no such Jacobian variety is simple.

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Keywords
Jacobian varieties, Hurwitz curves, projective special linear group, representation theory
Mathematical Subject Classification 2010
Primary: 14H40, 14H37, 20G05
Milestones
Received: 5 February 2015
Revised: 8 July 2015
Accepted: 20 July 2015
Published: 6 July 2016

Communicated by Nigel Boston
Authors
Allison Fischer
Department of Mathematics and Statistics
Grinnell College
Grinnell, IA 50112
United States
Mouchen Liu
Department of Mathematics and Statistics
Grinnell College
Grinnell, IA 50112
United States
Jennifer Paulhus
Department of Mathematics and Statistics
Grinnell College
Grinnell, IA 50112
United States