Symplectic singularities
Algebraic Geometry
2009-10-31 v1
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 .
Cite
@article{arxiv.math/9903070,
title = {Symplectic singularities},
author = {A. Beauville},
journal= {arXiv preprint arXiv:math/9903070},
year = {2009}
}
Comments
9 pages, Plain TeX