Duke Mathematical Journal

Symplectic invariance of uniruled affine varieties and log Kodaira dimension

Mark McLean

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

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Duke Math. J., Volume 163, Number 10 (2014), 1929-1964.

First available in Project Euclid: 8 July 2014

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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

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