{
  "id": "1202.6528",
  "version": "v3",
  "published": "2012-02-29T12:27:26.000Z",
  "updated": "2013-05-22T12:56:48.000Z",
  "title": "Stability of tautological bundles on the Hilbert scheme of two points on a surface",
  "authors": [
    "Malte Wandel"
  ],
  "comment": "14 pages, minors corrections of typos, replaced Lemma 2.2 by Def 2.2 and Prop. 2.3, to appear in Nag. Math. J",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let (X,H) be a polarized smooth projective surface satisfying H^1(X,O_X)=0 and let F be either a rank one torsion-free sheaf or a rank two {\\mu}H-stable vector bundle on X. Assume that c_1(F)/=0. In this article it is shown that the rank two, respectively rank four tautological sheaf F^{[2]} associated with F on the Hilbert square X^{[2]} is {\\mu}-stable with respect to a certain polarization.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-05-22T12:56:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14J28",
      "14J60",
      "14F05"
    ],
    "keywords": [
      "hilbert scheme",
      "tautological bundles",
      "smooth projective surface satisfying",
      "vector bundle",
      "hilbert square"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.6528W"
    }
  }
}