{
  "id": "math/9803120",
  "version": "v1",
  "published": "1998-03-25T10:10:17.000Z",
  "updated": "1998-03-25T10:10:17.000Z",
  "title": "McKay correspondence and Hilbert schemes in dimension three",
  "authors": [
    "Yukari Ito",
    "Hiraku Nakajima"
  ],
  "comment": "35 pages, 6 figures, latex2e with amsart, graphics, epic and eepic",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Let $G$ be a nontrivial finite subgroup of $\\SL_n(\\C)$. Suppose that the quotient singularity $\\C^n/G$ has a crepant resolution $\\pi\\colon X\\to \\C^n/G$ (i.e. $K_X = \\shfO_X$). There is a slightly imprecise conjecture, called the McKay correspondence, stating that there is a relation between the Grothendieck group (or (co)homology group) of $X$ and the representations (or conjugacy classes) of $G$ with a ``certain compatibility'' between the intersection product and the tensor product (see e.g. \\cite{Maizuru}). The purpose of this paper is to give more precise formulation of the conjecture when $X$ can be given as a certain variety associated with the Hilbert scheme of points in $\\C^n$. We give the proof of this new conjecture for an abelian subgroup $G$ of $\\SL_3(\\C)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-03-25T10:10:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E15",
      "14E45",
      "14E05",
      "13D15",
      "32S05",
      "20C05"
    ],
    "keywords": [
      "hilbert scheme",
      "mckay correspondence",
      "nontrivial finite subgroup",
      "precise formulation",
      "tensor product"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......3120I"
    }
  }
}