{
  "id": "math/0403122",
  "version": "v3",
  "published": "2004-03-07T14:54:17.000Z",
  "updated": "2007-03-06T17:33:33.000Z",
  "title": "Parametrization of Sing(Theta) for a Fano 3-fold of genus 7 by moduli of vector bundles",
  "authors": [
    "Atanas Iliev",
    "Dimitri Markushevich"
  ],
  "comment": "Final version; minor corrections",
  "journal": "Asian J. Math. 11, No. 3, 427-458 (2007)",
  "categories": [
    "math.AG"
  ],
  "abstract": "According to Mukai, any prime Fano threefold X of genus 7 is a linear section of the spinor tenfold in the projectivized half-spinor space of Spin(10). The orthogonal linear section of the spinor tenfold is a canonical genus-7 curve G, and the intermediate Jacobian J(X) is isomorphic to the Jacobian of G. It is proven that, for a generic X, the Abel-Jacobi map of the family of elliptic sextics on X factors through the moduli space of rank-2 vector bundles with c_1=-K_X and deg c_2=6 and that the latter is birational to the singular locus of the theta divisor of J(X).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-03-06T17:33:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J30"
    ],
    "keywords": [
      "vector bundles",
      "spinor tenfold",
      "parametrization",
      "prime fano threefold",
      "orthogonal linear section"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3122I"
    }
  }
}