{
  "id": "math/9903070",
  "version": "v1",
  "published": "1999-03-12T09:41:32.000Z",
  "updated": "1999-03-12T09:41:32.000Z",
  "title": "Symplectic singularities",
  "authors": [
    "A. Beauville"
  ],
  "comment": "9 pages, Plain TeX",
  "doi": "10.1007/s002229900043",
  "categories": [
    "math.AG"
  ],
  "abstract": "We discuss a particular class of rational Gorenstein singularities, which we call symplectic. A normal variety V has symplectic singularities if its smooth part carries a closed symplectic 2-form whose pull-back in any resolution X --> V extends to a holomorphic 2-form on X . Our main result is the classification of isolated symplectic singularities with smooth projective tangent cone. They are in one-to-one correspondence with simple complex Lie algebras: to a Lie algebra g corresponds the singularity at 0 of the closure of the minimal (nonzero) nilpotent adjoint orbit in g .",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-03-12T09:41:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singularity",
      "simple complex lie algebras",
      "rational gorenstein singularities",
      "smooth projective tangent cone",
      "nilpotent adjoint orbit"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2000,
      "month": "Mar",
      "volume": 139,
      "number": 3,
      "pages": 541
    },
    "note": {
      "typesetting": "Plain TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000InMat.139..541B"
    }
  }
}