{
  "id": "0707.0983",
  "version": "v2",
  "published": "2007-07-06T14:41:46.000Z",
  "updated": "2007-12-10T13:55:56.000Z",
  "title": "Moduli spaces of coherent systems of small slope on algebraic curves",
  "authors": [
    "S. B. Bradlow",
    "O. Garcia-Prada",
    "V. Mercat",
    "V. Munoz",
    "P. E. Newstead"
  ],
  "comment": "27 pages; minor presentational changes and typographical corrections",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $C$ be an algebraic curve of genus $g\\ge2$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections of $E$. The stability of the coherent system depends on a parameter $\\alpha$. We study the geometry of the moduli space of coherent systems for $0<d\\le2n$. We show that these spaces are irreducible whenever they are non-empty and obtain necessary and sufficient conditions for non-emptiness.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-12-10T13:55:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14D20",
      "14H51"
    ],
    "keywords": [
      "moduli space",
      "algebraic curve",
      "small slope",
      "algebraic vector bundle",
      "coherent system depends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.0983B"
    }
  }
}