Applications of the affine structures on the Teichmüller spaces

2014/02/23 by Kefeng Liu, Yang Shen, Liu, Kefeng +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1402.5570

openalex publication_date 2014/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 the 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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