  A conjecture by Yves Andre and Frans Oort says that closed subvarieties of
Shimura varieties that contain a Zariski dense subset of special points are
subvarieties of Hodge type. We prove this in the case where the subvariety is a
curve that contains infinitely many special points that lie in one Hecke orbit.
Via work of Juergen Wolfart, Paula Cohen and Gisbert Wuestholz, this result has
an application to algebraicity of values of hypergeometric functions.
