Transcendence and CM on Borcea–Voisin towers of Calabi–Yau manifolds

TextThis paper is a sequel to [32], in which we showed the validity of a special case of a conjecture of Green, Griffiths and Kerr [14] for certain families of Calabi–Yau manifolds over Hermitian symmetric domains. Our results are analogues of a celebrated theorem of Th. Schneider [25] on the transcendence of values of the elliptic modular function, and its generalization to the context of abelian varieties in [5] and [29]. In the present paper, we apply related techniques to examples of families of Calabi–Yau varieties from the work of Rohde [24], and in particular to Borcea–Voisin towers. Our results fit into the broader context of transcendence theory for variations of Hodge structure of higher weight.VideoFor a video summary of this paper, please visit http://youtu.be/9ZGYejBStJk.