A symplectic singularity is a complex normal variety whose smooth locus carries a holomorphic symplectic form, meaning a closed form that is a holomorphic differential form of degree 2 and is nondegenerate at each point. The form extends to a holomorphic differential form of degree 2 on a resolution of singularities. 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
Holomorphic Differential Form, Normal Variety, Resolution of Singularities, Symplectic Form, 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