#### 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