{
  "id": "0710.4978",
  "version": "v4",
  "published": "2007-10-26T02:37:37.000Z",
  "updated": "2009-02-02T14:43:29.000Z",
  "title": "Limits of log canonical thresholds",
  "authors": [
    "Tommaso de Fernex",
    "Mircea Mustata"
  ],
  "comment": "26 pages; revised version, to appear in Ann. Sci. Ecole Norm. Sup",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let T_n denote the set of log canonical thresholds of pairs (X,Y), with X a nonsingular variety of dimension n, and Y a nonempty closed subscheme of X. Using non-standard methods, we show that every limit of a decreasing sequence in T_n lies in T_{n-1}, proving in this setting a conjecture of Koll\\'{a}r. We also show that T_n is a closed subset in the set of real numbers; in particular, every limit of log canonical thresholds on smooth varieties of fixed dimension is a rational number. As a consequence of this property, we see that in order to check Shokurov's ACC Conjecture for all T_n, it is enough to show that 1 is not a point of accumulation from below of any T_n. In a different direction, we interpret the ACC Conjecture as a semi-continuity property for log canonical thresholds of formal power series.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-02-02T14:43:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "03H05",
      "14E30"
    ],
    "keywords": [
      "log canonical thresholds",
      "check shokurovs acc conjecture",
      "formal power series",
      "rational number",
      "nonempty closed subscheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.4978D"
    }
  }
}