nLab
symplectic singularities.

A symplectic singularity is a normal algebraic variety XX such that some (equivalently any) resolution of singularities of XX carries an algebraic 2-form Ω\Omega which is closed, and non-degenerate on the regular locus of the resolution.

A symplectic resolution is a resolution X˜X\tilde X\to X where the 2-form is closed and non-degenerate on all of X˜\tilde X. A symplectic resolution is necessarily Calabi-Yau.

A conical symplectic resolution is an affine symplectic singularity which carries a conical 𝔾 m\mathbb{G}_m-action (one with non-negative weights on the coordinate ring of XX, and zero-weight space spanned by 11) that acts on the symplectic form on the regular locus with weight n>0n\gt 0.

Created on February 17, 2012 at 23:10:42. See the history of this page for a list of all contributions to it.