{
  "id": "1502.04040",
  "version": "v1",
  "published": "2015-02-13T16:06:45.000Z",
  "updated": "2015-02-13T16:06:45.000Z",
  "title": "Hypersurfaces that are not stably rational",
  "authors": [
    "Burt Totaro"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that a wide class of hypersurfaces in all dimensions are not stably rational. Namely, for all d at least about 2n/3, a very general complex hypersurface of degree d in P^{n+1} is not stably rational. The statement generalizes Colliot-Thelene and Pirutka's theorem that very general quartic 3-folds are not stably rational. The result covers all the degrees in which Kollar proved that a very general hypersurface is non-rational, and a bit more. For example, very general quartic 4-folds are not stably rational, whereas it was not even known whether these varieties are rational.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-13T16:06:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E08",
      "14J45",
      "14J70"
    ],
    "keywords": [
      "stably rational",
      "general quartic",
      "general complex hypersurface",
      "statement generalizes colliot-thelene",
      "wide class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150204040T"
    }
  }
}