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2016 | OriginalPaper | Chapter

Applications of the Affine Structures on the Teichmüller Spaces

Authors : Kefeng Liu, Yang Shen, Xiaojing Chen

Published in: Geometry and Topology of Manifolds

Publisher: Springer Japan

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Abstract

We prove the existence of global sections trivializing the Hodge bundles on the Hodge metric completion space of the Torelli space of Calabi–Yau manifolds, a global splitting property of these Hodge bundles. We also prove that a compact Calabi–Yau manifold can not be deformed to its complex conjugate. These results answer certain open questions in the subject. A general result about certain period map to be bi-holomorphic from the Hodge metric completion space of the Torelli space of Calabi–Yau type manifolds to their period domains is proved and applied to the cases of K3 surfaces, cubic fourfolds, and hyperkähler manifolds.

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Metadata
Title
Applications of the Affine Structures on the Teichmüller Spaces
Authors
Kefeng Liu
Yang Shen
Xiaojing Chen
Copyright Year
2016
Publisher
Springer Japan
DOI
https://doi.org/10.1007/978-4-431-56021-0_3

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