{
  "id": "math/0302209",
  "version": "v1",
  "published": "2003-02-18T16:43:14.000Z",
  "updated": "2003-02-18T16:43:14.000Z",
  "title": "Theta functions on the moduli space of parabolic bundles",
  "authors": [
    "Francesca Gavioli"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a smooth projective connected curve of genus $g \\ge 2$ and let I be a finite set of points of X. Fix a parabolic structure on I for rank r vector bundles on X. Let $M^{par}$ denote the moduli space of parabolic semistable bundles and let $L^{par}$ denote the parabolic determinant bundle. In this paper we show that the n-th tensor power line bundle ${L^{par}}^n$ on the moduli space $M^{par}$ is globally generated, as soon as the integer n is such that $n \\ge [\\frac{r^2}{4}]$. In order to get this bound, we construct a parabolic analogue of the Quot scheme and extend the result of Popa and Roth on the estimate of its dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-02-18T16:43:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14F05",
      "14D20",
      "14H42"
    ],
    "keywords": [
      "moduli space",
      "theta functions",
      "parabolic bundles",
      "n-th tensor power line bundle",
      "parabolic determinant bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2209G"
    }
  }
}