On the symplectic invariance of log Kodaira dimension

Abstract

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.

31 pages, 2 figures

References in corpus (2)

• Birational cobordism invariance of uniruled symplectic manifolds
• Rationally connected $3$-folds and symplectic geometry

Cited by in corpus (1)

• Symplectic Divisorial Capping in Dimension 4