{
  "id": "1206.1990",
  "version": "v2",
  "published": "2012-06-10T02:58:49.000Z",
  "updated": "2013-09-30T03:49:09.000Z",
  "title": "On a generalization of the Mukai conjecture for Fano fourfolds",
  "authors": [
    "Kento Fujita"
  ],
  "comment": "16 pages. v2: title changed, add references",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a complex Fano manifold of dimension n. Let s(X) be the sum of l(R)-1 for all the extremal rays of X, the edges of the cone NE(X) of curves of X, where l(R) denotes the minimum of (-K_X \\cdot C) for all rational curves C whose class [C] belongs to R. We show that s(X)\\leq n if n\\leq 4. And for n\\leq 4, we completely classify the case the equality holds. This is a refinement of the Mukai conjecture on Fano fourfolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-30T03:49:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "14E30",
      "14J35"
    ],
    "keywords": [
      "fano fourfolds",
      "mukai conjecture",
      "generalization",
      "complex fano manifold",
      "extremal rays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.1990F"
    }
  }
}