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

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.