{
  "id": "1102.3637",
  "version": "v2",
  "published": "2011-02-17T17:03:17.000Z",
  "updated": "2011-02-24T21:54:26.000Z",
  "title": "Semistable vector bundles and Tannaka duality from a computational point of view",
  "authors": [
    "Almar Kaid",
    "Ralf Kasprowitz"
  ],
  "comment": "34 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We develop a semistability algorithm for vector bundles which are given as a kernel of a surjective morphism between splitting bundles on the projective space over an algebraically closed field K. This class of bundles is a generalization of syzygy bundles. We show how to implement this algorithm in a computer algebra system. Further we give applications, mainly concerning the computation of Tannaka dual groups of stable vector bundles of degree 0 on the projective space and on certain smooth complete intersection curves. We also use our algorithm to close an open case left in a recent work of L. Costa, P. Macias Marques and R. M. Miro-Roig regarding the stability of the syzygy bundle of general forms. Finally, we apply our algorithm to provide a computational approach to tight closure. All algorithms are implemented in the computer algebra system CoCoA.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-24T21:54:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J60",
      "14Q15",
      "13P10"
    ],
    "keywords": [
      "semistable vector bundles",
      "tannaka duality",
      "computational point",
      "smooth complete intersection curves",
      "syzygy bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.3637K"
    }
  }
}