{
  "id": "math/0408318",
  "version": "v2",
  "published": "2004-08-23T22:28:05.000Z",
  "updated": "2004-11-24T00:08:28.000Z",
  "title": "The moduli space of rank-3 vector bundles with trivial determinant over a curve of genus 2 and duality",
  "authors": [
    "Quang Minh Nguyen"
  ],
  "comment": "20 pages. v2",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let SU_X(3) be the moduli space of semi-stable vector bundles of rank 3 and trivial determinant on a curve X of genus 2. It maps onto P^8 and the map is a double cover branched over a sextic hypersurface called the Coble sextic. In the dual P^8 there is a unique cubic hypersurface, the Coble cubic, singular exactly along the abelian surface of degree 1 line bundles on X. We give a new proof that these two hypersurfaces are dual. As an immediate corollary, we derive a Torelli-type result.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-11-24T00:08:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14E05",
      "14J70"
    ],
    "keywords": [
      "trivial determinant",
      "moduli space",
      "unique cubic hypersurface",
      "sextic hypersurface",
      "semi-stable vector bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8318N"
    }
  }
}