{
  "id": "math/0410252",
  "version": "v4",
  "published": "2004-10-10T08:52:57.000Z",
  "updated": "2006-03-02T19:46:11.000Z",
  "title": "Factorial threefolds and Shokurov vanishing",
  "authors": [
    "Ivan Cheltsov"
  ],
  "comment": "22 pages, extended version, to appear in Sbornik: Mathematics",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "We prove the factoriality of the following nodal threefolds: a complete intersection of hypersurfaces $F$ and $G\\subset\\mathbb{P}^{5}$ of degree $n$ and $k$ respectively, where $G$ is smooth, $|\\mathrm{Sing}(F\\cap G)|\\leqslant(n+k-2)(n-1)/5$, $n\\geqslant k$; a double cover of a smooth hypersurface $F\\subset\\mathbb{P}^{4}$ of degree $n$ branched over a surface that is cut out on $F$ by a hypersurface $G$ of degree $2r\\geqslant n$, and $|\\mathrm{Sing}(F\\cap G)|\\leqslant(2r+n-2)r/4$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-03-02T19:46:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J30",
      "14J17",
      "14M10"
    ],
    "keywords": [
      "factorial threefolds",
      "shokurov vanishing",
      "nodal threefolds",
      "complete intersection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10252C"
    }
  }
}