{
  "id": "1010.5906",
  "version": "v4",
  "published": "2010-10-28T09:44:58.000Z",
  "updated": "2011-12-19T20:50:39.000Z",
  "title": "Degenerations of K3 Surfaces of Degree Two",
  "authors": [
    "Alan Thompson"
  ],
  "comment": "Final version. Accepted for publication by the Transactions of the American Mathematical Society",
  "journal": "Trans. Amer. Math. Soc. 366 (2014), No. 1, 219-243",
  "doi": "10.1090/S0002-9947-2013-05759-5",
  "categories": [
    "math.AG"
  ],
  "abstract": "We consider a semistable degeneration of K3 surfaces, equipped with an effective divisor that defines a polarisation of degree two on a general fibre. We show that the map to the relative log canonical model of the degeneration maps every fibre to either a sextic hypersurface in P(1,1,1,3) or a complete intersection of degree (2,6) in P(1,1,1,2,3). Furthermore, we find an explicit description of the hypersurfaces and complete intersections that can arise, thereby giving a full classification of the possible singular fibres.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-12-19T20:50:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D06",
      "14J28",
      "14E30",
      "43.40.Le",
      "42.81.Pa",
      "07.05.Hd"
    ],
    "keywords": [
      "k3 surfaces",
      "complete intersection",
      "full classification",
      "general fibre",
      "singular fibres"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011AIPC.1335....1T"
    }
  }
}