Affine structure on the Teichmuller spaces and period maps for Calabi-Yau manifolds.

摘要

In this thesis, we prove that the Hodge metric completion of the Teichmuller space of polarized and marked Calabi--Yau manifolds is a complex affine manifold. As applications, we show that the extended period map from the completion space is injective into the period domain, that the completion space is a bounded domain of holomorphy and admits a complete Kahler--Einstein metric.