{
  "id": "math/0301215",
  "version": "v1",
  "published": "2003-01-20T14:32:16.000Z",
  "updated": "2003-01-20T14:32:16.000Z",
  "title": "On the Irreducibility of Commuting Varieties of Nilpotent Matrices",
  "authors": [
    "R. Basili"
  ],
  "comment": "LaTex, 27 pages, to appear in J. Algebra",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Given an nxn nilpotent matrix over an algebraically closed field K, we prove some properties of the set of all the nxn nilpotent matrices over K which commute with it. Then we give a proof of the irreducibility of the variety of all the pairs (A,B) of nxn nilpotent matrices over K if either char K = 0 or char K isn't less than n/2. We get as a consequence a proof of the irreducibility of the local Hilbert scheme of n points of a smooth algebraic surface over K with the previous condition on char K.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-01-20T14:32:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "commuting varieties",
      "irreducibility",
      "nxn nilpotent matrices",
      "nxn nilpotent matrix",
      "local hilbert scheme"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......1215B"
    }
  }
}