{
  "id": "0712.3873",
  "version": "v2",
  "published": "2007-12-22T17:33:40.000Z",
  "updated": "2011-01-06T07:46:38.000Z",
  "title": "On the uniqueness of elliptic K3 surfaces with maximal singular fibre",
  "authors": [
    "Matthias Schuett",
    "Andreas Schweizer"
  ],
  "comment": "20 pages; v2: refereed version with some corrections and additions; author addresses and bibliography updated",
  "journal": "Annales de l'institut Fourier, 63 no. 2 (2013), p. 689-713",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We explicitly determine the elliptic K3 surfaces with a maximal singular fibre. If the characteristic of the ground field is different from 2, for each of the two possible maximal fibre types, $I_{19}$ and $I^*_{14}$, the surface is unique. In characteristic 2 the maximal fibre types are $I_{18}$ and $I^*_{13}$, and there exist two (resp. one) one-parameter families of such surfaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-06T07:46:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J27",
      "14J28",
      "11G05"
    ],
    "keywords": [
      "elliptic k3 surfaces",
      "maximal singular fibre",
      "maximal fibre types",
      "uniqueness",
      "ground field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3873S"
    }
  }
}