A family of Jacobians with definite quaternionic multiplication

We investigate explicitly a family of hyperelliptic curves of genus four whose Jacobians have definite quaternionic multiplication. This family has many interesting features, including: they give infinitely many examples where the ell-adic monodromy groups are disconnected over the field of definition of the endomorphism ring. This is joint work with Victoria Cantoral-Farfan and Davide Lombardo.