  We prove that a Shimura curve in the Siegel modular variety is not
generically contained in the open Torelli locus as long as the rank of unitary
part in its canonical Higgs bundle satisfies a numerical upper bound. As an
application we show that the Coleman-Oort conjecture holds for Shimura curves
associated to partial corestriction upon a suitable choice of parameters, which
generalizes a construction due to Mumford.
