  This paper is a sequel to a paper by the author and Marvin D. Tretkoff
(reference [49]), in which we showed the validity of a special case of a
conjecture of Green, Griffths and Kerr for certain families of Calabi-Yau
manifolds over Hermitian symmetric domains. These results are analogues of a
celebrated theorem of Th. Schneider on the transcendence of values of the
elliptic modular function, and its generalization to the context of abelian
varieties by the author, Shiga and Wolfart. In the present paper, we apply
related techniques to many of the examples of families of Calabi-Yau varieties
with dense sets of CM fibers in the work of Rohde, and in particular to
Borcea-Voisin towers. Our results fit into a broader context of transcendence
theory for variations of Hodge structure of higher weight.
