{
  "id": "math/0309277",
  "version": "v1",
  "published": "2003-09-17T13:41:02.000Z",
  "updated": "2003-09-17T13:41:02.000Z",
  "title": "Stabilité des fibrés $Λ^{p}E_{L}$ et condition de Raynaud",
  "authors": [
    "Olivier Schneider"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $C$ be a smooth curve of genus $g \\geq 2$ on $\\C$. Let $L$ be a line bundle on $C$ generated by its global sections and let $E_{L}$ be the dual of the kernel of the evaluation map $e_{L}$. We are studying here the relation between the stability the fact that the bundle is verifying a condition $(R)$ introduced by Raynaud : we prove that $E_{L}$ is semi stable when $C$ is general. We also prove that $E_{L}$ is verifying $(R)$ when $\\deg(L) \\geq 2g$ or when $L$ is generic. Finally we prove that for each $p$ in $\\{2,..., \\mathrm{rg}(E_{L})-2\\}$, if $\\deg(L) \\geq 2g+2$ then $\\Lambda^{p}E_{L}$ is not verifying $(R)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-17T13:41:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth curve",
      "line bundle",
      "global sections",
      "evaluation map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9277S"
    }
  }
}