{
  "id": "math/0205171",
  "version": "v1",
  "published": "2002-05-15T12:12:35.000Z",
  "updated": "2002-05-15T12:12:35.000Z",
  "title": "Multiplicities and log canonical threshold",
  "authors": [
    "Tommaso de Fernex",
    "Lawrence Ein",
    "Mircea Mustata"
  ],
  "comment": "13 pages; AMS-LaTeX",
  "journal": "J. Alg. Geom. 13 (2004), 603-615.",
  "categories": [
    "math.AG"
  ],
  "abstract": "If R is a local ring of dimension n, of a smooth complex variety, and if I is a zero dimensional ideal in R, then we prove that e(I)\\geq n^n/lc(I)^n. Here e(I) is the Samuel multiplicity along I, and lc(I) is the log canonical threshold of (R,I). We show that equality is achieved if and only if the integral closure of I is a power of the maximal ideal. When I is an arbitrary ideal, but n=2, we give a similar bound involving the Segre numbers of I.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-05-15T12:12:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "14C17"
    ],
    "keywords": [
      "log canonical threshold",
      "zero dimensional ideal",
      "smooth complex variety",
      "samuel multiplicity",
      "integral closure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......5171D"
    }
  }
}