{
  "id": "math/0207305",
  "version": "v3",
  "published": "2002-07-31T18:42:27.000Z",
  "updated": "2003-08-03T11:57:24.000Z",
  "title": "Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of abelian threefolds",
  "authors": [
    "Vassil Kanev"
  ],
  "comment": "43 pages, latex2e, some typos corrected, references updated, to appear in Annali di Matematica Pura ed Applicata",
  "journal": "Ann. Mat. Pura Appl. (4) Vol. 183 (2004), pp. 333 - 374.",
  "doi": "10.1007/s10231-003-0098-9",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove that the moduli spaces A_3(D) of polarized abelian threefolds with polarizations of types D=(1,1,2), (1,2,2), (1,1,3) or (1,3,3) are unirational. The result is based on the study of families of simple coverings of elliptic curves of degree 2 or 3 and on the study of the corresponding period mappings associated with holomorphic differentials with trace 0. In particular we prove the unirationality of the Hurwitz space H_{3,A}(Y) which parameterizes simply branched triple coverings of an elliptic curve Y with determinants of the Tschirnhausen modules isomorphic to A^{-1}.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-08-03T11:57:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14K10",
      "14H30",
      "14D07"
    ],
    "keywords": [
      "elliptic curve",
      "hurwitz space",
      "moduli spaces",
      "abelian threefolds",
      "parameterizes simply branched triple coverings"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......7305K"
    }
  }
}