{
  "id": "1112.1163",
  "version": "v5",
  "published": "2011-12-06T05:58:06.000Z",
  "updated": "2016-01-22T16:52:49.000Z",
  "title": "A Global Torelli Theorem for Calabi-Yau Manifolds",
  "authors": [
    "Kefeng Liu",
    "Yang Shen",
    "Andrey Todorov"
  ],
  "comment": "An error is corrected by using the Torelli space and its Hodge metric completion",
  "categories": [
    "math.AG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-01-08T16:05:38.000Z",
      "abstract": "We prove that the period map from the Teichmuller space of polarized and marked 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 and global holomorphic affine flat coordinates on the Teichmuller space.",
      "comment": "27 pages. We give a direct proof of the existence of the holomorphic affine structure on the Teichm\\\"uller space of Calabi-Yau manifolds",
      "journal": null,
      "doi": null,
      "authors": [
        "Feng Guan",
        "Kefeng Liu",
        "Andrey Todorov"
      ]
    },
    {
      "version": "v5",
      "updated": "2016-01-22T16:52:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global torelli theorem",
      "global holomorphic affine flat coordinates",
      "teichmuller space",
      "holomorphic affine structure",
      "marked calabi-yau manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1163L"
    }
  }
}