{
  "id": "1206.5491",
  "version": "v3",
  "published": "2012-06-24T13:27:45.000Z",
  "updated": "2013-07-02T19:23:48.000Z",
  "title": "Asymptotics of the Yang-Mills Flow for Holomorphic Vector Bundles Over Kähler Manifolds: The Canonical Structure of the Limit",
  "authors": [
    "Benjamin Sibley"
  ],
  "comment": "New version. Exposition improved and minor errors corrected based on comments from the referee. Acknowledgement added. Main content is unchanged. Final version to be published in Crelle's Journal. arXiv admin note: text overlap with arXiv:math/0410055 by other authors",
  "categories": [
    "math.DG"
  ],
  "abstract": "In the following article we study the limiting properties of the Yang-Mills flow associated to a holomorphic vector bundle E over an arbitrary compact K\\\"ahler manifold (X,{\\omega}). In particular we show that the flow is determined at infinity by the holomorphic structure of E. Namely, if we fix an integrable unitary reference connection A_0 defining the holomorphic structure, then the Yang-Mills flow with initial condition A_0, converges (away from an appropriately defined singular set) in the sense of the Uhlenbeck compactness theorem to a holomorphic vector bundle E_{\\infty}, which is isomorphic to the associated graded object of the Harder-Narasimhan-Seshadri filtration of (E,A_0). Moreover, E_{\\infty} extends as a reflexive sheaf over the singular set as the double dual of the associated graded object. This is an extension of previous work in the cases of 1 and 2 complex dimensions and proves the general case of a conjecture of Bando and Siu.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-02T19:23:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "holomorphic vector bundle",
      "yang-mills flow",
      "kähler manifolds",
      "canonical structure",
      "holomorphic structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1120063,
      "adsabs": "2012arXiv1206.5491S"
    }
  }
}