  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 .
