{
  "id": "math/0107182",
  "version": "v11",
  "published": "2001-07-24T23:38:06.000Z",
  "updated": "2011-01-16T21:13:17.000Z",
  "title": "Hyperholomorpic connections on coherent sheaves and stability",
  "authors": [
    "Misha Verbitsky"
  ],
  "comment": "37 pages, version 11, reference updated, corrected many minor errors and typos found by the referee",
  "journal": "Cent. Eur. J. Math., 2011, 9(3), 535-557",
  "doi": "10.2478/s11533-011-0016-0",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "Let $M$ be a hyperkaehler manifold, and $F$ a torsion-free and reflexive coherent sheaf on $M$. Assume that $F$ (outside of its singularities) admits a connection with a curvature which is invariant under the standard SU(2)-action on 2-forms. If the curvature is square-integrable, then $F$ is stable and its singularities are hyperkaehler subvarieties in $M$. Such sheaves (called hyperholomorphic sheaves) are well understood. In the present paper, we study sheaves admitting a connection with SU(2)-invariant curvature which is not necessarily square-integrable. This situation arises often, for instance, when one deals with higher direct images of holomorphic bundles. We show that such sheaves are stable.",
  "revisions": [
    {
      "version": "v11",
      "updated": "2011-01-16T21:13:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coherent sheaves",
      "hyperholomorpic connections",
      "higher direct images",
      "reflexive coherent sheaf",
      "situation arises"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......7182V"
    }
  }
}