Invariant Hilbert schemes and desingularizations of symplectic reductions for classical groups
Résumé
Let G be a classical subgroup of GL(V) acting on the symplectic vector space W=n'V \oplus n'V*, and \mu: W \rightarrow Lie(G)* the corresponding moment map. In this article, we use the theory of invariant Hilbert schemes to construct canonical desingularizations of the irreducible components of the symplectic reduction \mu^{-1}(0)//G for classes of examples where G=GL(V), O(V), or Sp(V). It is known that such components are isomorphic to closures of nilpotent orbits in simple Lie algebras, and we determine all the cases where the Hilbert-Chow morphism is a symplectic desingularization.
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