{
  "id": "math/0306275",
  "version": "v1",
  "published": "2003-06-18T19:26:49.000Z",
  "updated": "2003-06-18T19:26:49.000Z",
  "title": "Some schemes related to the commuting variety",
  "authors": [
    "Allen Knutson"
  ],
  "comment": "9 pages",
  "journal": "J. Algebraic Geom. 14 (2005) 283-294",
  "categories": [
    "math.AG"
  ],
  "abstract": "The_commuting variety_ is the pairs of NxN matrices (X,Y) such that XY = YX. We introduce the_diagonal commutator scheme_, {(X,Y) : XY-YX is diagonal}, which we prove to be a reduced complete intersection, one component of which is the commuting variety. (We conjecture there to be only one other component.) The diagonal commutator scheme has a flat degeneration to the scheme {(X,Y) : XY lower triangular, YX upper triangular}, which is again a reduced complete intersection, this time with n! components (one for each permutation). The degrees of these components give interesting invariants of permutations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-18T19:26:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M10",
      "15A27"
    ],
    "keywords": [
      "commuting variety",
      "reduced complete intersection",
      "diagonal commutator scheme",
      "yx upper triangular"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6275K"
    }
  }
}