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15 July 2014 Symplectic invariance of uniruled affine varieties and log Kodaira dimension
Mark McLean
Duke Math. J. 163(10): 1929-1964 (15 July 2014). DOI: 10.1215/00127094-2738748

Abstract

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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Mark McLean. "Symplectic invariance of uniruled affine varieties and log Kodaira dimension." Duke Math. J. 163 (10) 1929 - 1964, 15 July 2014. https://doi.org/10.1215/00127094-2738748

Information

Published: 15 July 2014
First available in Project Euclid: 8 July 2014

zbMATH: 1312.53107
MathSciNet: MR3229045
Digital Object Identifier: 10.1215/00127094-2738748

Subjects:
Primary: 53D35
Secondary: 14R05, 53D45

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 10 • 15 July 2014
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