Abelian varieties isogenous to a Jacobian

We define a notion of Weyl CM points in the moduli space A(g,1) of g-dimensional principally polarized abelian varieties and show that the Andre-Oort conjecture (or the GRH) implies the following statement: for any closed subvariety X subset of(not equal) A(g,1) over Q(a), there exists a Weyl special point [(B, mu)] is an element of A(g,1)(Q(a)) such that B is not isogenous to the abelian variety A underlying any point [(A, lambda)] is an element of X. The title refers to the case when g >= 4 and X is the Torelli locus; in this case Tsimerman has proved the statement unconditionally. The notion of Weyl special points is generalized to the context of Shimura varieties, and we prove a corresponding conditional statement with the ambient space A(g,1) replaced by a general Shimura variety.