{
  "id": "math/0302204",
  "version": "v1",
  "published": "2003-02-18T11:27:24.000Z",
  "updated": "2003-02-18T11:27:24.000Z",
  "title": "Nilpotent commuting varieties of reductive Lie algebras",
  "authors": [
    "Alexander Premet"
  ],
  "comment": "25 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove that the nilpotent commuting variety of a reductive Lie algebra over an algebraically closed field of good characteristic is equidimensional. In characteristic zero, this confirms a conjecture of Vladimir Baranovsky. As a by-product, we obtain tat the punctual (local) Hilbert scheme parametrising the ideals of colength $n$ in $k[[X,Y]]$ is irreducible over any algebraically closed field $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-02-18T11:27:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nilpotent commuting variety",
      "reductive lie algebra",
      "algebraically closed field",
      "characteristic zero",
      "vladimir baranovsky"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00222-003-0315-6",
      "journal": "Inventiones Mathematicae",
      "year": 2003,
      "month": "Dec",
      "volume": 154,
      "number": 3,
      "pages": 653
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003InMat.154..653P"
    }
  }
}