{
  "id": "math/0405011",
  "version": "v2",
  "published": "2004-05-01T19:59:03.000Z",
  "updated": "2004-08-26T18:09:32.000Z",
  "title": "Birational geometry of Fano direct products",
  "authors": [
    "Aleksandr V. Pukhlikov"
  ],
  "comment": "38 pages, LaTeX. This is the final enlarged version of the paper",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove birational superrigidity of direct products $V=F_1\\times...\\times F_K$ of primitive Fano varieties of the following two types: either $F_i\\subset{\\mathbb P}^M$ is a general hypersurface of degree $M$, $M\\geq 6$, or $F_i\\stackrel{\\sigma}{\\to}{\\mathbb P}^M$ is a general double space of index 1, $M\\geq 3$. In particular, each structure of a rationally connected fiber space on $V$ is given by a projection onto a direct factor. The proof is based on the connectedness principle of Shokurov and Koll\\' ar and the technique of hypertangent divisors.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-08-26T18:09:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E05",
      "14E07",
      "14E08"
    ],
    "keywords": [
      "fano direct products",
      "birational geometry",
      "birational superrigidity",
      "hypertangent divisors",
      "connectedness principle"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}