A normal variety is called a symplectic variety? if its smooth part admits a holomorphic symplectic form, whose pull-back to any resolution extends to a holomorphic 2-form. If this 2-form is itself symplectic, the given resolution is called a symplectic resolution. More generally, an algebraic variety is said to have symplectic singularities if every point in the variety has a neighborhood which carries a symplectic structure.
Symplectic resolutions are analogous to hyper Kähler manifolds?.
The term was introduced in
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