{
  "id": "math/0408274",
  "version": "v2",
  "published": "2004-08-20T05:35:46.000Z",
  "updated": "2005-01-17T04:12:21.000Z",
  "title": "Birational geometry of symplectic resolutions of nilpotent orbits II",
  "authors": [
    "Yoshinori Namikawa"
  ],
  "comment": "Main results hold for arbitrary simple Lie algebras, that is, the conjectual part in the previous version is established",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we shall study symplectic resolutions of a nilpotent orbit closure of a complex simple Lie algebra \\g. We shall introduce an equivalence relation in the set of parabolic subgroups of $G$ in terms of marked Dynkin diagrams. We start with a nilpotent orbit closure which admits a Springer resolution with a parabolic subgroup $P_0$ of $G$. Then we prove that all symplectic resolution of the nilpotent closure are Springer resolutions with $P$ which are equivalent to $P_0$. Here all symplectic resolutions are connected by Mukai flops. We need three types of Mukai flops (types A, D and E_6) in connecting symplectic resolutions. In particular, Mukai flops of type E_6 are new. All arguments of Part I : math.AG/0404072 which use flags, are replaced by those which use only Dynkin diagrams.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-01-17T04:12:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birational geometry",
      "mukai flops",
      "nilpotent orbit closure",
      "parabolic subgroup",
      "springer resolution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8274N"
    }
  }
}