A Global Torelli Theorem for Calabi-Yau Manifolds

Kefeng Liu; Yang Shen; Andrey Todorov

A Global Torelli Theorem for Calabi-Yau Manifolds

Algebraic Geometry 2016-12-13 v6

Authors: Kefeng Liu , Yang Shen , Andrey Todorov

Abstract

We describe the proof that the period map from the Torelli space of Calabi-Yau manifolds to the classifying space of polarized Hodge structures is an embedding. The proof is based on the constructions of holomorphic affine structure on the Teichm\"uller space and Hodge metric completion of the Torelli space. A canonical global holomorphic section of the holomorphic $(n, 0)$ class on the Teichm\"uller space is constructed.

Keywords

Torelli theorem Calabi-Yau manifolds period map polarized Hodge structures Teichmuller space holomorphic affine structure Hodge metric

Cite

@article{arxiv.1112.1163,
  title  = {A Global Torelli Theorem for Calabi-Yau Manifolds},
  author = {Kefeng Liu and Yang Shen and Andrey Todorov},
  journal= {arXiv preprint arXiv:1112.1163},
  year   = {2016}
}

Comments

An error is corrected by using the Torelli space and its Hodge metric completion

A Global Torelli Theorem for Calabi-Yau Manifolds

Abstract

Keywords

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