{
  "id": "math/0511312",
  "version": "v4",
  "published": "2005-11-14T20:03:33.000Z",
  "updated": "2011-07-23T14:30:26.000Z",
  "title": "Clemens' conjecture: part I",
  "authors": [
    "Bin Wang"
  ],
  "comment": "This paper has been withdrawn by the author. withdraw the article. It needs to be rewritten",
  "categories": [
    "math.AG"
  ],
  "abstract": "This is a series of two papers in which we solve the Clemens conjecture: there are only finitely many smooth rational curves of each degree in a generic quintic threefold. In this first paper, we deal with a family of smooth Calabi-Yau threefolds f_\\epsilon for a small complex number \\epsilon. We give an geometric obstruction, deviated quasi-regular deformations B_b of c_\\epsilon, to a deformation of the rational curve c_\\epsilon in a Calabi-Yau threefold f_\\epsilon.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-07-23T14:30:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32",
      "14C25"
    ],
    "keywords": [
      "smooth rational curves",
      "generic quintic threefold",
      "smooth calabi-yau threefolds",
      "small complex number",
      "deviated quasi-regular deformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}