{
  "id": "math/0404453",
  "version": "v1",
  "published": "2004-04-26T05:30:24.000Z",
  "updated": "2004-04-26T05:30:24.000Z",
  "title": "Symplectic desingularization of moduli space of sheaves on a K3 surface",
  "authors": [
    "Young-Hoon Kiem"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a projective K3 surface with generic polarization $\\cO_X(1)$ and let $M_c=M(2,0,c)$ be the moduli space of semistable torsion-free sheaves on $X$ of rank 2, with Chern classes $c_1=0$ and $c_2=c$. When $c=2n\\ge 4$ is even, $M_c$ is a singular projective variety. We show that there is no symplectic desingularization of $M_{2n}$ if $\\frac{n a_n}{2n-3}$ is not an integer where $a_n$ is the Euler number of the Hilbert scheme $X^{[n]}$ of $n$ points in $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-26T05:30:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14F25",
      "14F42"
    ],
    "keywords": [
      "moduli space",
      "symplectic desingularization",
      "generic polarization",
      "semistable torsion-free sheaves",
      "projective k3 surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4453K"
    }
  }
}