# nLab symplectic singularities.

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

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

A conical symplectic resolution is an affine symplectic singularity which carries a conical $\mathbb{G}_m$-action (one with non-negative weights on the coordinate ring of $X$, and zero-weight space spanned by $1$) that acts on the symplectic form on the regular locus with weight $n\gt 0$.

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