Higher dimensional Shimura varieties in the Prym loci of ramified double covers

In this paper, we construct Shimura subvarieties of dimension bigger than one of the moduli space ${\mathsf{A}}_p^{\delta }$ of δ-polarized abelian varieties of dimension p, which are generically contained in the Prym loci of (ramified) double covers. The idea is to adapt the techniques already used to construct Shimura curves in the Prym loci to the higher dimensional case, namely, to use families of Galois covers of ${\mathbb{P}}^1$. The case of abelian covers is treated in detail, since in this case, it is possible to make explicit computations that allow to verify a sufficient condition for such a family to yield a Shimura subvariety of ${\mathsf{A}}_p^{\delta }$.