Hodge Metric Completion of the Moduli Space of Calabi-Yau Manifolds

摘要

We review our results about period maps for Calabi-Yau manifolds. We show that there are holomorphic affine structures on the Teichmiilcer, Torelli space and its Hodge metric completion of Calabi-Yau manifolds. We also show that the extended period map from the completion space of the Torelli space is injective, and the completion space is a bounded domain of holomorphy and admits a complete K?hlerEinstein metric. Moreover, we get the global Torelli theorem on the Torelli space of Calabi-Yau manifolds as a corollary.