Global Torelli Theorem for Projective Manifolds of Calabi-Yau Type

Abstract

We prove that the period maps from the Torelli space and the moduli space with level $m$ structure of Calabi-Yau type manifolds to the corresponding period domain of polarized Hodge structures are injective. The proof is based on the construction of holomorphic affine structure on the Teichmüller space and the construction of the completion space of the Torelli space with respect to the Hodge metric.

Some clarifications are added and two simpler proofs of Theorem 3.11 are given

References in corpus (2)

• Fano manifolds of Calabi-Yau type
• Hodge metric completion of the moduli space of Calabi-Yau manifolds

Cited by in corpus (6)

• Special Geometry and the Swampland
• Swampland geometry and the gauge couplings
• Hodge metric completion of the moduli space of Calabi-Yau manifolds
• From local Torelli to global Torelli
• Moduli spaces as ball quotients I, local theory
• Boundedness of the Images of Period Maps