{
  "id": "0812.3014",
  "version": "v2",
  "published": "2008-12-16T09:56:48.000Z",
  "updated": "2009-06-25T12:37:42.000Z",
  "title": "On the classification of degree 1 elliptic threefolds with constant $j$-invariant",
  "authors": [
    "Remke Kloosterman"
  ],
  "comment": "A new proof for Proposition 3.5 is provided; several minor changes",
  "categories": [
    "math.AG"
  ],
  "abstract": "We describe the possible Mordell-Weil groups for degree 1 elliptic threefold with rational base and constant $j$-invariant. Moreover, we classify all such elliptic threefolds if the $j$-invariant is nonzero. We can use this classification to describe a class of singular hypersurfaces in $\\Ps(2,3,1,1,1)$ that admit no variation of Hodge structure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-06-25T12:37:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic threefold",
      "classification",
      "singular hypersurfaces",
      "rational base",
      "hodge structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.3014K"
    }
  }
}