{
  "id": "1510.07232",
  "version": "v1",
  "published": "2015-10-25T11:23:42.000Z",
  "updated": "2015-10-25T11:23:42.000Z",
  "title": "Algebraic dimension of twistor spaces whose fundamental system is a pencil",
  "authors": [
    "Nobuhiro Honda",
    "Bernd Kreussler"
  ],
  "comment": "22 pages, 1 figure",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "We show that the algebraic dimension of a twistor space over n#CP^2 cannot be two if n>4 and the fundamental system (i.e. the linear system associated to the half-anti-canonical bundle, which is available on any twistor space) is a pencil. This means that if the algebraic dimension of a twistor space on n#CP^2, n>4, is two, then the fundamental system either is empty or consists of a single member. The existence problem for a twistor space on n#CP^2 with algebraic dimension two is open for n>4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-25T11:23:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "twistor space",
      "algebraic dimension",
      "fundamental system",
      "linear system",
      "single member"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007232H"
    }
  }
}