Shimura subvarieties in the Prym locus of ramified Galois coverings

Abstract

We study Shimura (special) subvarieties in the moduli space Ap,D of complex abelian varieties of dimension p and polarization type D. These subvarieties arise from families of covers compatible with a fixed group action on the base curve such that the quotient of the base curve by the group is isomorphic to P1. We give a criterion for the image of these families under the Prym map to be a special subvariety and, using computer algebra, obtain 210 Shimura subvarieties contained in the Prym locus.