Slodowy Slices and Universal Poisson Deformations

Abstract

We classify the nilpotent orbits in a simple Lie algebra for which the restriction of the adjoint quotient map to a Slodowy slice is the universal Poisson deformation of its central fibre. This generalises work of Brieskorn and Slodowy on subregular orbits. In particular, we find in this way new singular symplectic hypersurfaces of dimension 4 and 6.

29 p. Minor changes. Final version. To appear in Compositio Mathematica

References in corpus (3)

• Poisson deformations of affine symplectic varieties II
• Poisson deformations of affine symplectic varieties
• Birational geometry and deformations of nilpotent orbits

Cited by in corpus (15)

• Vertex operator algebras, Higgs branches, and modular differential equations
• The Hasse Diagram of the Moduli Space of Instantons
• Diagram automorphisms of quiver varieties
• Counting resolutions of symplectic quotient singularities
• Poisson deformations and birational geometry
• Singularities of nilpotent orbit closures
• Actions on the quiver -- Discrete quotients on the Coulomb branch
• Equivalence of symplectic singularities
• The universal Poisson deformation of hypertoric varieties and some classification results
• Four-dimensional conical symplectic hypersurfaces
• Stability conditions for Slodowy slices and real variations of stability
• Universal filtered quantizations of nilpotent Slodowy slices
• Deformations of hyperkähler cones
• Weights of Semiregular Nilpotents in Simple Lie Algebras of D Type
• Arrangements, multiderivations, and adjoint quotient map of type ADE