{
  "id": "math/0204261",
  "version": "v2",
  "published": "2002-04-22T07:12:35.000Z",
  "updated": "2002-07-25T09:47:53.000Z",
  "title": "Families of abelian varieties over curves with maximal Higgs field",
  "authors": [
    "Eckart Viehweg",
    "Kang Zuo"
  ],
  "comment": "13 pages, Latex, two minor errors corrected, the content of this note became part of math.AG/0207228",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "Let f:X-->Y be a semi-stable family of complex abelian varieties over a curve Y of genus q, and smooth over the complement of s points. If F(1,0) denotes the non-flat (1,0) part of the corresponding variation of Hodge structures, the Arakelov inequalities say that 2deg(F(1,0)) is bounded from above by g=rank(F(1,0))(2q-2+s). We show that for s>0 families reaching this bound are isogenous to the g-fold product of a modular family of elliptic curves, and a constant abelian variety. The content of this note became part of the article \"A characterization of certain Shimura curves in the moduly stack of abelian varieties\" (math.AG/0207228), where we also handle the case s=0.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-07-25T09:47:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K10",
      "14D05",
      "14D07"
    ],
    "keywords": [
      "maximal higgs field",
      "complex abelian varieties",
      "constant abelian variety",
      "arakelov inequalities",
      "shimura curves"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......4261V"
    }
  }
}