{
  "id": "1109.6938",
  "version": "v4",
  "published": "2011-09-30T19:56:14.000Z",
  "updated": "2013-10-25T16:05:23.000Z",
  "title": "Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems",
  "authors": [
    "Asher Auel",
    "Marcello Bernardara",
    "Michele Bolognesi"
  ],
  "comment": "43 pages, changes made and some material added and corrected in sections 1, 4, and 5; this is the final version accepted for publication at Journal de Math\\'ematiques Pures et Appliqu\\'ees",
  "journal": "Journal de math\\'ematiques pures et appliqu\\'ees 102 (2014), pp. 249--291",
  "doi": "10.1016/j.matpur.2013.11.009",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X -> Y be a fibration whose fibers are complete intersections of two quadrics. We develop new categorical and algebraic tools---a theory of relative homological projective duality and the Morita invariance of the even Clifford algebra under quadric reduction by hyperbolic splitting---to study semiorthogonal decompositions of the bounded derived category of X. Together with new results in the theory of quadratic forms, we apply these tools in the case where X -> Y has relative dimension 1, 2, or 3, in which case the fibers are curves of genus 1, Del Pezzo surfaces of degree 4, or Fano threefolds, respectively. In the latter two cases, if Y is the projective line over an algebraically closed field of characteristic zero, we relate rationality questions to categorical representability of X.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-10-25T16:05:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05",
      "14E08",
      "11E08",
      "11E20",
      "11E88",
      "14F22",
      "14J26",
      "14M17",
      "15A66"
    ],
    "keywords": [
      "complete intersections",
      "clifford algebra",
      "derived category",
      "rationality problems",
      "hyperbolic splitting-to study semiorthogonal decompositions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.6938A"
    }
  }
}