  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.
