{
  "id": "math/0209094",
  "version": "v1",
  "published": "2002-09-09T15:42:37.000Z",
  "updated": "2002-09-09T15:42:37.000Z",
  "title": "Elliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7",
  "authors": [
    "A. Iliev",
    "D. Markushevich"
  ],
  "comment": "37 pages",
  "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). It is proven that the moduli space of stable rank-2 vector bundles with Chern classes c_1=1,c_2=5 on a generic X is isomorphic to the curve of genus 7 obtained by taking an orthogonal linear section of the spinor tenfold. This is an inverse of Mukai's result on the isomorphism of a non-abelian Brill--Noether locus on a curve of genus 7 to a Fano threefold of genus 7. An explicit geometric construction of both isomorphisms and a similar result for K3 surfaces of genus 7 are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-09-09T15:42:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J30"
    ],
    "keywords": [
      "prime fano threefold",
      "vector bundles",
      "elliptic curves",
      "spinor tenfold",
      "orthogonal linear section"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9094I"
    }
  }
}