{
  "id": "math/9902145",
  "version": "v1",
  "published": "1999-02-25T09:19:01.000Z",
  "updated": "1999-02-25T09:19:01.000Z",
  "title": "Restriction of the Poincaré bundle to a Calabi-Yau hypersurface",
  "authors": [
    "Indranil Biswas",
    "Leticia Brambila-Paz"
  ],
  "comment": "AMSLaTex file. To appear in Crelles J",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $\\cMx$ be the moduli space of stable vector bundles of rank $n\\geq 3$ and determinant $\\xi$ over a connected Riemann surface $X$, with $n$ and $d(\\xi)$ coprime. Let $D$ be a Calabi-Yau hypersurface of $\\cMx$. Denote by $U_D$ the restriction of the universal bundle to $X\\times D$. It is shown that the restriction $(U_D)_x$ to $x\\times D$ is stable, for any $x\\in X$. Furthermore, for a general curve the connected component of the moduli space of semistable sheaves over $D$, containing $(U_D)_x$, is isomorphic to $X$. It is also shown that $U_D$ is stable for any polarisation, and the connected component of the moduli space of semistable sheaves over $X\\times D$, containing $U_D$, is isomorphic to the Jacobian. Moreover, this is an isomorphism of polarised varieties, and hence such a moduli spaces determine the Reimann surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-02-25T09:19:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calabi-yau hypersurface",
      "restriction",
      "moduli spaces determine",
      "semistable sheaves",
      "connected component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......2145B"
    }
  }
}