{
  "id": "math/0209392",
  "version": "v3",
  "published": "2002-09-27T21:57:11.000Z",
  "updated": "2003-02-22T16:07:50.000Z",
  "title": "Jet schemes, log discrepancies and Inversion of Adjunction",
  "authors": [
    "Lawrence Ein",
    "Mircea Mustata",
    "Takehiko Yasuda"
  ],
  "comment": "17 pages, AMS-LaTeX; v.2: the statement of Corollary 2.4 is corrected, Theorems 2.5 and 2.6 from the previous version have been combined in one stronger statement; v.3: final version, to appear in Invent. Math",
  "journal": "Invent. Math. 153 (2003), 119-135.",
  "doi": "10.1007/s00222-003-0298-3",
  "categories": [
    "math.AG"
  ],
  "abstract": "We use the theory of motivic integration for singular spaces to give a characterization of minimal log discrepencies in terms of the codimension of certain subsets of spaces of arcs. This is done for arbitrary pairs $(X,Y)$, with $X$ normal and Q-Gorenstein. As a first application, we prove a precise version of Inversion of Adjunction, in the case when the ambient variety is smooth. Another application concerns the semicontinuity of minimal log discrepancies on smooth varieties.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-02-22T16:07:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "14E30",
      "14E15",
      "14B10"
    ],
    "keywords": [
      "jet schemes",
      "adjunction",
      "minimal log discrepancies",
      "minimal log discrepencies",
      "singular spaces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2003,
      "month": "Sep",
      "volume": 153,
      "number": 3,
      "pages": 519
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003InMat.153..519E"
    }
  }
}