{
  "id": "1304.4495",
  "version": "v4",
  "published": "2013-04-16T15:40:54.000Z",
  "updated": "2014-12-30T18:06:53.000Z",
  "title": "On linear systems and a conjecture of D. C. Butler",
  "authors": [
    "U. N. Bhosle",
    "L. Brambila-Paz",
    "P. E. Newstead"
  ],
  "comment": "Final version accepted for publication in Internat. J. math",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $C$ be a smooth irreducible projective curve of genus $g$ and $L$ a line bundle of degree $d$ generated by a linear subspace $V$ of $H^0(L)$ of dimension $n+1$. We prove a conjecture of D. C. Butler on the semistability of the kernel of the evaluation map $V\\otimes{\\mathcal O}_C\\to L$ and obtain new results on the stability of this kernel. The natural context for this problem is the theory of coherent systems on curves and our techniques involve wall crossing formulae in this theory.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-29T10:27:21.000Z",
      "abstract": "Let $C$ be a smooth irreducible projective curve of genus $g$ and $L$ a line bundle of degree $d$ generated by a linear subspace $V$ of $H^0(L)$ of dimension $n+1$. We obtain new results on the stability of the kernel of the evaluation map.",
      "comment": "Final version submitted for publication. Substantial rewriting and expansion; major results unchanged; minor improvements in subsidiary results; additional results on stability of kernel bundles. Additional references added for background purposes",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-12-30T18:06:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60"
    ],
    "keywords": [
      "linear systems",
      "conjecture",
      "evaluation map",
      "smooth irreducible projective curve",
      "linear subspace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.4495B"
    }
  }
}