A finiteness theorem on symplectic singularities
  For positive integers N and d, there are only finite number of conical symplectic varieties of dimension 2d with maximal weights N, up to isomorphism.   The maximal weight of a conical symplectic variety X is, by definition, the maximal weight of the minimal homogeneous generators of the coordinate ring R of X. 
Yoshinori Namikawa
math.AG