Shimura subvarieties via endomorphisms

Abstract

We show the existence of two new Shimura subvarieties of ${\mathcal{A}}_2,{\mathcal{A}}_3$ generically contained in the Torelli locus. They provide the first examples of Shimura subvarieties obtained by means of Jacobians carrying non-trivial endomorphisms not directly induced by the automorphisms of the curves. We also obtain a new example of a Shimura subvariety of ${\mathcal{A}}_4$ generically contained in the Prym locus.