Applications of the affine structures on the Teichmller spaces

Kefeng Liu Yang Shen Xiaojing Chen

Algebraic Geometry mathscidoc:1912.43102

59-79, 2016
We prove the existence of global sections trivializing the Hodge bundles on the Hodge metric completion space of the Torelli space of CalabiYau manifolds, a global splitting property of these Hodge bundles. We also prove that a compact CalabiYau 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 CalabiYau type manifolds to their period domains is proved and applied to the cases of K3 surfaces, cubic fourfolds, and hyperkhler manifolds.
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@inproceedings{kefeng2016applications,
  title={Applications of the affine structures on the Teichmller spaces},
  author={Kefeng Liu, Yang Shen, and Xiaojing Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111545148893662},
  pages={59-79},
  year={2016},
}
Kefeng Liu, Yang Shen, and Xiaojing Chen. Applications of the affine structures on the Teichmller spaces. 2016. pp.59-79. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111545148893662.
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