Jacobian varieties of Hurwitz curves with automorphism group PSL(2,q)

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.