{
  "id": "math/0408408",
  "version": "v6",
  "published": "2004-08-30T14:04:55.000Z",
  "updated": "2005-09-19T18:49:22.000Z",
  "title": "Bernstein-Sato polynomials of arbitrary varieties",
  "authors": [
    "Nero Budur",
    "Mircea Mustata",
    "Morihiko Saito"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We introduce the notion of Bernstein-Sato polynomial of an arbitrary variety (which is not necessarily reduced nor irreducible), using the theory of V-filtrations of M. Kashiwara and B. Malgrange. We prove that the decreasing filtration by multiplier ideals coincides essentially with the restriction of the V-filtration. This implies a relation between the roots of the Bernstein-Sato polynomial and the jumping coefficients of the multiplier ideals, and also a criterion for rational singularities in terms of the maximal root of the polynomial in the case of a reduced complete intersection. These are generalizations of the hypersurface case. We can calculate the polynomials explicitly in the case of monomial ideals.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2005-09-19T18:49:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S40"
    ],
    "keywords": [
      "bernstein-sato polynomial",
      "arbitrary variety",
      "maximal root",
      "hypersurface case",
      "multiplier ideals coincides"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8408B"
    }
  }
}