{
  "id": "math/0308006",
  "version": "v1",
  "published": "2003-08-01T15:47:43.000Z",
  "updated": "2003-08-01T15:47:43.000Z",
  "title": "Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)",
  "authors": [
    "Vassil Kanev"
  ],
  "comment": "28 pages, amslatex, to appear in Mathematische Nachrichten",
  "journal": "Math. Nachr. Vol. 278 (2005), pp. 154 - 172.",
  "doi": "10.1002/mana.200310233",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove that the moduli space A_3(1,1,4) of polarized abelian threefolds with polarization of type (1,1,4) is unirational. By a result of Birkenhake and Lange this implies the unirationality of the isomorphic moduli space A_3(1,4,4). The result is based on the study the Hurwitz space H_{4,n}(Y) of quadruple coverings of an elliptic curve Y simply branched in n points. We prove the unirationality of its codimension one subvariety H^{0}_{4,A}(Y) which parametrizes quadruple coverings \\pi:X --> Y with Tschirnhausen modules isomorphic to A^{-1}, where A\\in Pic^{n/2}Y, and for which \\pi^*:J(Y)--> J(X) is injective. This is an analog of the result of Arbarello and Cornalba that the Hurwitz space H_{4,n}(P^1) is unirational.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-08-01T15:47:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K10",
      "14H10",
      "14H30"
    ],
    "keywords": [
      "hurwitz space",
      "elliptic curve",
      "abelian threefolds",
      "tschirnhausen modules isomorphic",
      "parametrizes quadruple coverings"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......8006K"
    }
  }
}