{
  "id": "1512.05681",
  "version": "v1",
  "published": "2015-12-17T17:24:57.000Z",
  "updated": "2015-12-17T17:24:57.000Z",
  "title": "Birational geometry of algebraic varieties, fibred into Fano double spaces",
  "authors": [
    "Aleksandr V. Pukhlikov"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We develop the quadratic technique of proving birational rigidity of Fano-Mori fibre spaces over a higher-dimensional base. As an application, we prove birational rigidity of generic fibrations into Fano double spaces of dimension $M\\geqslant 4$ and index one over a rationally connected base of dimension at most $\\frac12 (M-2)(M-1)$. An estimate for the codimension of the subset of hypersurfaces of a given degree in the projective space with a positive-dimensional singular set is obtained, which is close to the optimal one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-17T17:24:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E05",
      "14E07"
    ],
    "keywords": [
      "fano double spaces",
      "algebraic varieties",
      "birational geometry",
      "positive-dimensional singular set",
      "fano-mori fibre spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151205681P"
    }
  }
}