Abstract

Introducing special subvarieties in a moduli space of Calabi-Yau n-folds arising from non-rigid families, we discuss the finiteness, smoothness and uniformizations (n=3) of those subvarieties, and we formulate the precise statement for Shafarevich program for families of Calabi-Yau n-folds. This is a project started in joint paper with Viehweg and carried out in a recent joint work in progress with Ruiran Sun and Chenlong Yu.