{
  "id": "1204.0377",
  "version": "v3",
  "published": "2012-04-02T11:41:39.000Z",
  "updated": "2014-12-23T20:13:13.000Z",
  "title": "On the Commuting variety of a reductive Lie algebra and other related varieties",
  "authors": [
    "Jean-Yves Charbonnel",
    "Mouchira Zaiter"
  ],
  "comment": "According to Ting Xue and K. Vilonen, a result of the last version is not true, whence some modifications",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "In this note, we discuss some varieties which are constructed analogously to the isospectral commuting varieties. These varieties are subvarieties of varieties having very simple desingularizations. For instance, this is the case of the nullcone of any cartesian power of a reductive Lie algebra and we prove that it is normal. Moreover, as a byproduct of these investigations and a Ginzburg's result, we get that the normalizations of the isospectral commuting variety and the commuting variety have rational singularities.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-10T12:22:39.000Z",
      "abstract": "In this note, one discusses about some varieties which are constructed analogously to the isospectral commuting varieties. These varieties are subvarieties of varieties having very simple desingularizations. For instance, this is the case of the nullcone of any cartesian power of a reductive Lie algebra and one proves that it has rational singularities. Moreover, as a byproduct of these investigations and the Ginzburg's results, one gets that the normalizations of the isospectral commuting variety and the commuting variety have rational singularities.",
      "comment": "61 pages. Few modifications in the presentation. Some proofs are improved or corrected",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-12-23T20:13:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reductive lie algebra",
      "related varieties",
      "isospectral commuting variety",
      "rational singularities",
      "simple desingularizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.0377C"
    }
  }
}