Duke Mathematical Journal
- Duke Math. J.
- Volume 163, Number 10 (2014), 1929-1964.
Symplectic invariance of uniruled affine varieties and log Kodaira dimension
We introduce some definitions of uniruledness for affine varieties and use these ideas to show symplectic invariance of various algebraic invariants of affine varieties. For instance we show that if and are symplectomorphic smooth affine varieties, then any compactification of by a projective variety is uniruled if and only if any such compactification of is uniruled. If is acylic of dimension , then we show that has the same log Kodaira dimension as . If has dimension , has log Kodaira dimension , and satisfies some other conditions, then cannot be of log general type.
Duke Math. J., Volume 163, Number 10 (2014), 1929-1964.
First available in Project Euclid: 8 July 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]
Secondary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35] 14R05: Classification of affine varieties
McLean, Mark. Symplectic invariance of uniruled affine varieties and log Kodaira dimension. Duke Math. J. 163 (2014), no. 10, 1929--1964. doi:10.1215/00127094-2738748. https://projecteuclid.org/euclid.dmj/1404824305