{
  "id": "1205.4119",
  "version": "v2",
  "published": "2012-05-18T09:19:07.000Z",
  "updated": "2012-05-22T09:48:30.000Z",
  "title": "Moduli of sheaves and the Chow group of K3 surfaces",
  "authors": [
    "Kieran G. O'Grady"
  ],
  "comment": "Deleted a footnote and replaced it by a sentence in the main body of the paper",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a projective complex K3 surface. Beauville and Voisin singled out a 0-cycle c_X on X of degree 1: it is represented by any point lying on a rational curve in X. Huybrechts proved that the second Chern class of a rigid simple vector-bundle on X is a multiple of the Beauville-Voisin class c_X if certain hypotheses hold and he conjectured that the additional hypotheses are unnecessary. We believe that the following generalization of Huybrechts' conjecture holds. Let M and N be moduli spaces of stable pure sheaves on X (with fixed cohomological Chern characters) and suppose that they have the same dimension: then the set whose elements are second Chern classes of sheaves parametrized by the closure of M (in the corresponding moduli spaces of semistable sheaves) is equal to the set whose elements are second Chern classes of sheaves parametrized by the closure of N after a translation by a suitable multiple of c_X (so that degrees match). We will prove that the above statement holds under some additional assumptions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-22T09:48:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15"
    ],
    "keywords": [
      "chow group",
      "second chern classes",
      "moduli spaces",
      "projective complex k3 surface",
      "rigid simple vector-bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.4119O"
    }
  }
}