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From local Torelli to global Torelli

Kefeng Liu Yang Shen

Algebraic Geometry mathscidoc:1912.43103

arXiv preprint arXiv:1512.08384, 2015.12
We introduce the notions of strong local Torelli and T-class for polarized manifolds, and prove that strong local Torelli implies global Torelli theorem on the Torelli spaces for polarized manifolds in the T-class. We discuss many new examples of projective manifolds for which such global Torelli theorem holds. As applications we prove that, in these cases, a canonical completion of the Torelli space is a bounded pseudoconvex domain in complex Euclidean space, and show that generic Torelli implies global Torelli on moduli space with certain level structure.
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@inproceedings{kefeng2015from,
  title={From local Torelli to global Torelli},
  author={Kefeng Liu, and Yang Shen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111548013468663},
  booktitle={arXiv preprint arXiv:1512.08384},
  year={2015},
}
Kefeng Liu, and Yang Shen. From local Torelli to global Torelli. 2015. In arXiv preprint arXiv:1512.08384. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111548013468663.
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