A symplectic singularity is a normal complex algebraic variety whose smooth locus carries a holomorphic symplectic form that extends to a holomorphic two-form on a resolution of singularities. The form is closed and nondegenerate on the smooth locus. Its extension may be degenerate on the exceptional set. Extension on one resolution implies extension on every resolution (Beauville 2000). A symplectic resolution imposes nondegeneracy everywhere on the resolved space.
Symplectic Singularity
See also
Normal Variety, Resolution of Singularities, Symplectic Manifold, Symplectic ResolutionExplore with Wolfram|Alpha
References
Beauville, A. "Symplectic Singularities." Invent. Math. 139, 541-549, 2000. https://doi.org/10.1007/s002229900043.Cite this as:
Weisstein, Eric W. "Symplectic Singularity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SymplecticSingularity.html