On the symplectic invariance of log Kodaira dimension

2012/11/09 by Mark McLean, McLean, Mark
Mathematics · #14R05 (Secondary) #53D35 (Primary) 53D45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1211.2034

openalex publication_date 2012/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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