{
  "id": "math/0407100",
  "version": "v6",
  "published": "2004-07-07T11:26:38.000Z",
  "updated": "2005-04-10T06:30:01.000Z",
  "title": "Nonexistence of a crepant resolution of some moduli spaces of sheaves on a K3 surface",
  "authors": [
    "Jaeyoo Choy",
    "Young-Hoon Kiem"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $M_c=M(2,0,c)$ be the moduli space of O(1)-semistable rank 2 torsion-free sheaves with Chern classes $c_1=0$ and $c_2=c$ on a K3 surface $X$ where O(1) is a generic ample line bundle on $X$. When $c=2n\\geq4$ is even, $M_c$ is a singular projective variety equipped with a symplectic structure on the smooth locus. In this paper, we show that there is no crepant resolution of $M_{2n}$ for $n\\geq 3$. This implies that there is no symplectic desingularization.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2005-04-10T06:30:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D30",
      "14J60"
    ],
    "keywords": [
      "moduli space",
      "k3 surface",
      "crepant resolution",
      "nonexistence",
      "generic ample line bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7100C"
    }
  }
}