{
  "id": "math/0303198",
  "version": "v1",
  "published": "2003-03-17T10:10:14.000Z",
  "updated": "2003-03-17T10:10:14.000Z",
  "title": "Moduli spaces of SL(r)-bundles on singular irreducible curves",
  "authors": [
    "Xiaotao Sun"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a stable irreducible curve $X$ and a torsion free sheaf $L$ on $X$ of rank one and degree $d$, D.S. Nagaraj and C.S. Seshadri ([NS]) defined a closed subset $\\Cal U_X(r,L)$ in the moduli space of semistable torsion free sheaves of rank $r$ and degree $d$ on $X$. We prove that $\\Cal U_X(r,L)$ is irreducible, when a smooth curve $Y$ specializes to $X$ and a line bundle $\\Cal L$ on $Y$ specializes to $L$, the specialization of moduli space of semistable rank $r$ vector bundles on $Y$ with fixed determinant $\\Cal L$ has underlying set $\\Cal U_X(r,L)$. For rank 2 and 3, we show that there is a Cohen-Macaulay closed subscheme in the Gieseker space which represents a suitable moduli functor and has good specialization property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-03-17T10:10:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "singular irreducible curves",
      "torsion free sheaf",
      "semistable torsion free sheaves",
      "suitable moduli functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......3198S"
    }
  }
}