Invariant Hilbert schemes and desingularizations of symplectic reductions for classical groups

2013/03/12 by Ronan Terpereau, Terpereau, Ronan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.1007/s00209-013-1259-1

Abstract

Let G ⊂ GL(V) be a reductive algebraic subgroup acting on the symplectic vector space W=(V ⊕ V^*)^{⊕ m}, and let μ: W → Lie(G)^* be the corresponding moment map. In this article, we use the theory of invariant Hilbert schemes to construct a canonical desingularization of the symplectic reduction μ^-1(0)/ /G for classes of examples where G=GL(V), O(V), or Sp(V). For these classes of examples, μ^-1(0)/ /G is isomorphic to the closure of a nilpotent orbit in a simple Lie algebra, and we compare the Hilbert-Chow morphism with the (well-known) symplectic desingularizations of μ^-1(0)/ /G.

Citations

• INVARIANT HILBERT SCHEMES AND DESINGULARIZATIONS OF QUOTIENTS BY CLASSICAL GROUPS

Cited by

• INVARIANT HILBERT SCHEMES AND DESINGULARIZATIONS OF QUOTIENTS BY CLASSICAL GROUPS
• Invariant deformation theory of affine schemes with reductive group action

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