{
  "id": "0803.0722",
  "version": "v2",
  "published": "2008-03-05T17:57:10.000Z",
  "updated": "2008-03-18T15:23:20.000Z",
  "title": "Some remarks on varieties of pairs of commuting upper triangular matrices and an interpretation of commuting varieties",
  "authors": [
    "Roberta Basili"
  ],
  "comment": "Latex, 11 pages",
  "categories": [
    "math.AG",
    "math.OA"
  ],
  "abstract": "It is known that the variety of pairs of n x n commuting upper triangular matrices isn't a complete intersection for infinitely many values of n; we show that there exists m such that this happens if and only if n > m. We also show that m < 18 and that it could be found by determining the dimension of the variety of pairs of commuting strictly upper triangular matrices. Then we define a natural map from the variety of pairs of commuting n x n matrices onto a subvariety defined by linear equations of the grassmannian of subspaces of codimension 2 of a vector space of dimension n x n.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-03-18T15:23:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A30",
      "14L30"
    ],
    "keywords": [
      "commuting varieties",
      "commuting upper triangular matrices isnt",
      "interpretation",
      "commuting strictly upper triangular matrices"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.0722B"
    }
  }
}