{
  "id": "math/0310040",
  "version": "v3",
  "published": "2003-10-03T12:37:09.000Z",
  "updated": "2005-04-20T08:19:56.000Z",
  "title": "Semistability vs. nefness for (Higgs) vector bundles",
  "authors": [
    "U. Bruzzo",
    "D. Hernandez Ruiperez"
  ],
  "comment": "Comments: 20 pages, Latex2e, no figures. v2 includes a generalization to complex projective manifolds of any dimension. To appear in Diff. Geom. Appl",
  "journal": "Diff. Geom. Appl. 24 (2006) 403-416",
  "doi": "10.1016/j.difgeo.2005.12.007",
  "categories": [
    "math.AG"
  ],
  "abstract": "According to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-04-20T08:19:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14F05",
      "14H60"
    ],
    "keywords": [
      "vector bundle",
      "semistability",
      "higgs bundle",
      "higher-dimensional complex projective varieties",
      "locally-free higgs quotients"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10040B"
    }
  }
}