Flops and Poisson deformations of symplectic varieties

Details Flops and Poisson deformations of symplectic varieties Flops and Poisson deformations of symplectic varieties

2005-10-04

arxiv.org/abs/math/0510059v9

Publ. RIMS, Vol 44 (2008), 259-314

Mathematics

Algebraic Geometry

In the previous version, we claimed that singularities do not change under an arbitrary symplectic flop. But, this claim is no

Scientific paper

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 $X'$. If $X$ is non-singular, then $X'$ is non-singular, too. Moreover, when $Y$ has a good $C^*$-action, $X$ and $X'$ have the same kind of singularities.

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