{
  "id": "1508.06174",
  "version": "v1",
  "published": "2015-08-25T14:56:46.000Z",
  "updated": "2015-08-25T14:56:46.000Z",
  "title": "On the generalized commuting varieties of a reductive Lie algebra",
  "authors": [
    "Jean-Yves Charbonnel",
    "Mouchira Zaiter"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1204.0377, arXiv:1507.05419",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "The generalized commuting and isospectral commuting varieties of a reductive Lie algebra have been introduced in a preceding article. In this note, it is proved that their normalizations are Gorenstein with rational singularities. Moreover, their canonical modules are free of rank 1. In particular, the usual commuting variety is Gorenstein with rational singularities and its canonical module is free of rank 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-25T14:56:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reductive lie algebra",
      "generalized commuting varieties",
      "rational singularities",
      "canonical module",
      "usual commuting variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}