{
  "id": "math/0205317",
  "version": "v1",
  "published": "2002-05-30T11:59:38.000Z",
  "updated": "2002-05-30T11:59:38.000Z",
  "title": "Coherent systems and Brill-Noether theory",
  "authors": [
    "Steven Bradlow",
    "Oscar Garcia-Prada",
    "Vicente Muñoz",
    "Peter Newstead"
  ],
  "comment": "44 pages, Latex2e",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $C$ be a curve of genus $g\\geq 2$. A coherent system on $C$ consists of a pair $(E,V)$ where $E$ is an algebraic vector bundle of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of sections of $E$. The stability of the coherent systems depend on a parameter $\\tau$. We study the variation of the moduli space of coherent systems when we move the parameter. As an application, we analyse the cases $k=1,2,3$ and $n=2$ explicitly. For small values of $\\tau$, the moduli space of coherent systems is related to the Brill-Noether loci, the subspaces of the moduli space of stable bundles consisting of those bundles with a prescribed number of sections. The study of coherent systems is applied to find the dimension, irreducibility, and in some cases, the Picard group, of the Brill-Noether loci with $k\\leq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-05-30T11:59:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14H51",
      "14H60"
    ],
    "keywords": [
      "brill-noether theory",
      "moduli space",
      "brill-noether loci",
      "coherent systems depend",
      "algebraic vector bundle"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......5317B"
    }
  }
}