{
  "id": "math/9911161",
  "version": "v2",
  "published": "1999-11-21T21:23:07.000Z",
  "updated": "2000-05-03T17:46:25.000Z",
  "title": "Beyond a conjecture of Clemens",
  "authors": [
    "Ziv Ran"
  ],
  "comment": "Statements and proofs have been modified. In some cases the results are now stronger. In particular, we prove that a generic sextic 3-fold contains no rational or elliptic curves, and no nondegenerate curves of genus 2, which goes beyond Clemens' original conjecture",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove some lower bounds on certain twists of the canonical bundle of a codimension-2 subvariety of a generic hypersurface in projective space. In particular we prove that the generic sextic threefold contains no rational or elliptic curves and no nondegenerate curves of genus 2.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-05-03T17:46:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "generic sextic threefold contains",
      "generic hypersurface",
      "lower bounds",
      "elliptic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....11161R"
    }
  }
}