{
  "id": "1305.0537",
  "version": "v3",
  "published": "2013-05-02T19:03:08.000Z",
  "updated": "2014-10-01T09:41:55.000Z",
  "title": "Birational geometry of hypersurfaces in products of projective spaces",
  "authors": [
    "John Christian Ottem"
  ],
  "comment": "v3: Minor changes",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the birational properties of hypersurfaces in products of projective spaces. In the case of hypersurfaces in P^m x P^n, we describe their nef, movable and effective cones and determine when they are Mori dream spaces. Using this, we give new simple examples of non-Mori dream spaces and analogues of Mumford's example of a strictly nef line bundle which is not ample.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-10T11:12:15.000Z",
      "title": "Hypersurfaces in products of projective spaces and their birational geometry",
      "comment": "13 pages. 1 figure. v2: Main theorem considerably strengthened",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-01T09:41:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E05",
      "14C20",
      "14M99"
    ],
    "keywords": [
      "projective spaces",
      "birational geometry",
      "hypersurfaces",
      "strictly nef line bundle",
      "non-mori dream spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.0537O"
    }
  }
}