{
  "id": "1306.4838",
  "version": "v2",
  "published": "2013-06-20T11:59:29.000Z",
  "updated": "2016-04-28T12:10:35.000Z",
  "title": "Nested Punctual Hilbert Schemes and Commuting Varieties of Parabolic Subalgebras",
  "authors": [
    "Michael Bulois",
    "Laurent Evain"
  ],
  "comment": "43 pages",
  "journal": "Journal of Lie Theory, 2016, 26 (2), pp.497--533",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "It is known that the variety parametrizing pairs of commuting nilpotent matrices is irreducible and that this provides a proof of the irreducibility of the punctual Hilbert scheme in the plane. We extend this link to the nilpotent commuting variety of parabolic subalgebras of $M\\_n(\\K)$ and to the punctual nested Hilbert scheme. By this method, we obtain a lower bound on the dimension of these moduli spaces. We characterize the numerical conditions under which they are irreducible. In some reducible cases, we describe the irreducible components and their dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-20T11:59:29.000Z",
      "title": "Nested punctual Hilbert schemes and commuting varieties of parabolic subalgebras",
      "abstract": "It is known that the variety parametrizing pairs of commuting nilpotent matrices is irreducible and that this provides a proof of the irreducibility of the punctual Hilbert scheme in the plane. We extend this link to the nilpotent commuting variety of parabolic subalgebras of $M_n(\\K)$ and to the punctual nested Hilbert scheme. By this method, we obtain a lower bound on the dimension of these moduli spaces. We characterize the numerical conditions under which they are irreducible. In some reducible cases, we describe the irreducible components and their dimension.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-04-28T12:10:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nested punctual hilbert schemes",
      "parabolic subalgebras",
      "punctual nested hilbert scheme",
      "commuting nilpotent matrices",
      "nilpotent commuting variety"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.4838B"
    }
  }
}