{
  "id": "1504.03061",
  "version": "v1",
  "published": "2015-04-13T04:28:20.000Z",
  "updated": "2015-04-13T04:28:20.000Z",
  "title": "Geometry of some twistor spaces of algebraic dimension one",
  "authors": [
    "Nobuhiro Honda"
  ],
  "comment": "29 pages, 5 figures",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "It is shown that there exists a twistor space on the $n$-fold connected sum of complex projective planes $n\\mathbb{CP}^2$, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over $n\\mathbb{CP}^2$ for any $n\\ge 5$, while the latter kind of example is constructed over $5\\mathbb{CP}^2$. Both of these seem to be the first such example on $n\\mathbb{CP}^2$. The algebraic reduction in these examples is induced by the anti-canonical system of the twistor spaces. It is also shown that the former kind of twistor spaces contain a pair of non-normal Hopf surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-13T04:28:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic dimension",
      "algebraic reduction",
      "twistor spaces contain",
      "non-normal hopf surfaces",
      "fold connected sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150403061H"
    }
  }
}