{
  "id": "math/0512318",
  "version": "v1",
  "published": "2005-12-14T10:21:41.000Z",
  "updated": "2005-12-14T10:21:41.000Z",
  "title": "Vector bundles with a fixed determinant on an irreducible nodal curve",
  "authors": [
    "Usha N Bhosle"
  ],
  "comment": "7 pages",
  "journal": "Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 4, November 2005, pp. 445-451",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $M$ be the moduli space of generalized parabolic bundles (GPBs) of rank $r$ and degree $d$ on a smooth curve $X$. Let $M_{\\bar L}$ be the closure of its subset consisting of GPBs with fixed determinant ${\\bar L}$. We define a moduli functor for which $M_{\\bar L}$ is the coarse moduli scheme. Using the correspondence between GPBs on $X$ and torsion-free sheaves on a nodal curve $Y$ of which $X$ is a desingularization, we show that $M_{\\bar L}$ can be regarded as the compactified moduli scheme of vector bundles on $Y$ with fixed determinant. We get a natural scheme structure on the closure of the subset consisting of torsion-free sheaves with a fixed determinant in the moduli space of torsion-free sheaves on $Y$. The relation to Seshadri--Nagaraj conjecture is studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-14T10:21:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60"
    ],
    "keywords": [
      "fixed determinant",
      "irreducible nodal curve",
      "vector bundles",
      "torsion-free sheaves",
      "moduli space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12318B"
    }
  }
}