Hodge metric completion of the moduli space of Calabi-Yau manifolds

Abstract

In this paper, it is proved that the Hodge metric completion of the moduli space of polarized and marked Calabi-Yau manifolds, i.e. the Torelli space, is a complex affine manifold. As applications we prove that the period map from the Torelli space and the extended period map from its completion space, both are injective into the period domain, and that the completion space is a bounded domain of holomorphy with a complete Kähler-Einstein metric. As a corollary we show that the period map from the moduli space of polarized Calabi-Yau manifolds with level $m$ structure is also injective.

Some clarifications are added and two simpler proofs of Theorem 3.10 are given. arXiv admin note: text overlap with arXiv:1205.4207

References in corpus (2)

• Extremal degenerations of polarized Hodge structures
• Global Torelli Theorem for Projective Manifolds of Calabi-Yau Type

Cited by in corpus (8)

• Special Geometry and the Swampland
• Global Torelli Theorem for Projective Manifolds of Calabi-Yau Type
• Swampland geometry and the gauge couplings
• From local Torelli to global Torelli
• Boundedness of the images of period maps and applications
• Quantum Correction and the Moduli Spaces of Calabi-Yau Manifolds
• Boundedness of the Images of Period Maps
• Simultaneous normalization of period map and affine structures on moduli spaces