Symplectic singularities

Details Symplectic singularities Symplectic singularities

1999-03-12

arxiv.org/abs/math/9903070v1

Mathematics

Algebraic Geometry

9 pages, Plain TeX

Scientific paper

10.1007/s002229900043

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 .

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