{
  "id": "1106.0345",
  "version": "v2",
  "published": "2011-06-02T00:12:50.000Z",
  "updated": "2012-04-20T13:57:06.000Z",
  "title": "Mather discrepancy and the arc spaces",
  "authors": [
    "Shihoko Ishii"
  ],
  "comment": "Some explanations are added in the proof of the main theorem. final version, to appear in Annales de l'Institut Fourier",
  "categories": [
    "math.AG"
  ],
  "abstract": "The goal of this paper is a classification theorem of the singularities according to a new invariant, Mather discrepancy. On the other hand, we show some evidences convincing us that Mather discrepancy is a considerable invariant: By introducing new log-canonical threshold and minimal log-discrepancy by means of Mather discrepancy instead of usual discrepancy of canonical divisors, we obtain the formulas of the new log-canonical threshold in terms of arc spaces, inversion of adjunction for wider class of singularities than the known one, lower seimicontinuity of the new minimal log-discrepancy and the affirmative answer to a conjecture of Shokurov type; One advantage of the new invariants is that these are defined for arbitrary varieties (without q-Gorenstein property); These results include the known results for usual log-canonical threshold and minimal log-discrepancy.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-20T13:57:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E18",
      "14B05"
    ],
    "keywords": [
      "arc spaces",
      "minimal log-discrepancy",
      "mather discrepancy",
      "lower seimicontinuity",
      "wider class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0345I"
    }
  }
}