{
  "id": "1101.4763",
  "version": "v2",
  "published": "2011-01-25T10:14:39.000Z",
  "updated": "2012-08-17T15:57:28.000Z",
  "title": "Explicit Models for Threefolds Fibred by K3 Surfaces of Degree Two",
  "authors": [
    "Alan Thompson"
  ],
  "comment": "Early sections have been restructured and shortened. Assumptions required for the main construction have been weakened. Final version, accepted for publication by the Canadian Journal of Mathematics",
  "journal": "Canad. J. Math. 65 (2013), No. 4, 905-926",
  "doi": "10.4153/CJM-2012-037-2",
  "categories": [
    "math.AG"
  ],
  "abstract": "We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative log canonical model exists and can be explicitly reconstructed from a small set of data determined by the original fibration. Finally we prove a converse to the above statement: under certain assumptions, any such set of data determines a threefold that arises as the relative log canonical model of a threefold admitting a fibration by K3 surfaces of degree two.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-17T15:57:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J30",
      "14D06",
      "14E30",
      "14J28"
    ],
    "keywords": [
      "k3 surfaces",
      "explicit models",
      "threefolds",
      "relative log canonical model",
      "assumptions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.4763T"
    }
  }
}