{
  "id": "1112.1886",
  "version": "v4",
  "published": "2011-12-08T17:19:02.000Z",
  "updated": "2014-04-02T11:52:35.000Z",
  "title": "A GIT interpretration of the Harder-Narasimhan filtration",
  "authors": [
    "Tomas L. Gomez",
    "Ignacio Sols",
    "Alfonso Zamora"
  ],
  "comment": "19 pages; Comments of the referees and references added. The construction for holomorphic pairs (Sections 6 and 7 from previous version) will appear in a further publication. To appear in Rev. Mat Complutense",
  "doi": "10.1007/s13163-014-0149-3",
  "categories": [
    "math.AG"
  ],
  "abstract": "An unstable torsion free sheaf on a smooth projective variety gives a GIT unstable point in certain Quot scheme. To a GIT unstable point, Kempf associates a \"maximally destabilizing\" 1-parameter subgroup, and this induces a filtration of the torsion free sheaf. We show that this filtration coincides with the Harder-Narasimhan filtration.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-04-02T11:52:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14L24"
    ],
    "keywords": [
      "harder-narasimhan filtration",
      "git interpretration",
      "git unstable point",
      "unstable torsion free sheaf",
      "kempf associates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1886G"
    }
  }
}