Flops and Poisson deformations of symplectic varieties

Abstract

This is a local version of math.AG/0506534. We shall deal with the deformation of a convex symplectic variety $X$ instead of a projective one. The usual deformation does not work well in the convex case. Instead, we regard $X$ as a Poisson scheme and study its Poisson deformation. One of the application is the following: Let $Y$ be an affine symplectic variety, and assume that $Y$ has two $Q$-factorial crepant terminalizations $X$ and $X^{\prime }$. If $X$ is non-singular, then $X^{\prime }$ is non-singular, too. Moreover, when $Y$ has a good $C^{\ast }$-action, $X$ and $X^{\prime }$ have the same kind of singularities.

In the previous version, we claimed that singularities do not change under an arbitrary symplectic flop. But, this claim is not justified for lack of algebraization

Cited by in corpus (1)

• A survey on symplectic singularities and resolutions