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 $84\left(g-1\right)$. 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 $PSL\left(2,q\right)$. We present a decomposition of the Jacobian varieties for all curves of this type and prove that no such Jacobian variety is simple.

Keywords
Jacobian varieties, Hurwitz curves, projective special linear group, representation theory
Mathematical Subject Classification 2010
Primary: 14H40, 14H37, 20G05
Milestones
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