{
  "id": "1207.5697",
  "version": "v2",
  "published": "2012-07-24T13:39:20.000Z",
  "updated": "2013-04-27T00:14:48.000Z",
  "title": "New proofs of the Torelli theorems for Riemann surfaces",
  "authors": [
    "Kefeng Liu",
    "Quanting Zhao",
    "Sheng Rao"
  ],
  "comment": "A revised version, 21 pages; All comments are welcome",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "In this paper, by using the Kuranishi coordinates on the Teichm\\\"uller space and the explicit deformation formula of holomorphic one-forms on Riemann surface, we give an explicit expression of the period map and derive new differential geometric proofs of the Torelli theorems, both local and global, for Riemann surfaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-27T00:14:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann surface",
      "torelli theorems",
      "explicit deformation formula",
      "differential geometric proofs",
      "holomorphic one-forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.5697L"
    }
  }
}