  Suppose that A and B are symplectomorphic smooth affine varieties. If A is
acylic of dimension 2 then B has the same log Kodaira dimension as A. If the
dimension of A is 3, has log Kodaira dimension 2 and satisfies some other
conditions then B cannot be of log general type. We also show that if A and B
are symplectomorphic affine varieties of any dimension then any
compactification of A by a projective variety is uniruled if and only if any
such compactification of B is uniruled.
