{
  "id": "math/9911179",
  "version": "v2",
  "published": "1999-11-23T10:51:30.000Z",
  "updated": "2001-09-27T17:08:49.000Z",
  "title": "An introduction to motivic integration",
  "authors": [
    "Alastair Craw"
  ],
  "comment": "32 pages, 1 figure. Stringy E-function redefined and examples given in more detail. Also we present a proof of the cohomological McKay correspondence for a finite Abelian subgroup of SL(n,C) to illustrate the simplicity of Batyrev's approach in this case",
  "categories": [
    "math.AG"
  ],
  "abstract": "By associating a `motivic integral' to every complex projective variety X with at worst canonical, Gorenstein singularities, Kontsevich proved that, when there exists a crepant resolution of singularities Y of X, the Hodge numbers of Y do not depend upon the choice of the resolution. In this article we provide an elementary introduction to the theory of motivic integration, leading to a proof of the result described above. We calculate the motivic integral of several quotient singularities and discuss these calculations in the context of the cohomological McKay correspondence.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-09-27T17:08:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "motivic integration",
      "motivic integral",
      "complex projective variety",
      "cohomological mckay correspondence",
      "quotient singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....11179C"
    }
  }
}