{
  "id": "math/0307015",
  "version": "v2",
  "published": "2003-07-01T18:36:16.000Z",
  "updated": "2003-07-28T18:18:00.000Z",
  "title": "Cubic threefolds and abelian varieties of dimension five",
  "authors": [
    "Sebastian Casalaina-Martin",
    "Robert Friedman"
  ],
  "comment": "LaTeX, 34 pages, one theorem strengthened, improved historical discussion, references added",
  "categories": [
    "math.AG"
  ],
  "abstract": "This paper proves the following converse to a theorem of Mumford: Let $A$ be a principally polarized abelian variety of dimension five, whose theta divisor has a unique singular point, and suppose that the multiplicity of the singular point is three. Then $A$ is isomorphic as a principally polarized abelian variety to the intermediate Jacobian of a smooth cubic threefold. The method of proof is to analyze the possible singularities of the theta divisor of $A$, and eventually to show that $A$ is the Prym variety of a possibly singular plane quintic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-07-28T18:18:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J30",
      "14H40",
      "14C34",
      "14C35",
      "14K25"
    ],
    "keywords": [
      "principally polarized abelian variety",
      "theta divisor",
      "unique singular point",
      "smooth cubic threefold",
      "possibly singular plane quintic"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}