{
  "id": "1706.01356",
  "version": "v1",
  "published": "2017-06-05T14:50:00.000Z",
  "updated": "2017-06-05T14:50:00.000Z",
  "title": "On the rationality problem for quadric bundles",
  "authors": [
    "Stefan Schreieder"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that a wide class of smooth quadric bundles over rational bases are not stably rational. If the base has dimension n>1, then the possible fibre dimensions range from $2^{n-1}-1$ to $2^{n}-2$. For any r>2, this yields the first known smooth r-fold quadric bundles over rational bases which are not (stably) rational. In our proofs we introduce a generalization of the specialization method of Voisin and Colliot-Th\\'el\\`ene--Pirutka which avoids universally $CH_0$-trivial resolutions of singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-05T14:50:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E08",
      "14M20",
      "14J35",
      "14D06"
    ],
    "keywords": [
      "rationality problem",
      "rational bases",
      "smooth r-fold quadric bundles",
      "fibre dimensions range",
      "smooth quadric bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}