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On Eckl's pseudo-effective reduction map


Author: Brian Lehmann
Journal: Trans. Amer. Math. Soc. 366 (2014), 1525-1549
MSC (2010): Primary 14C20
DOI: https://doi.org/10.1090/S0002-9947-2013-05826-6
Published electronically: August 15, 2013
MathSciNet review: 3145741
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Abstract: Suppose that $ X$ is a complex projective variety and $ L$ is a pseudo-effective divisor. A numerical reduction map is a quotient of $ X$ by all subvarieties along which $ L$ is numerically trivial. We construct two variants: the $ L$-trivial reduction map and the pseudo-effective reduction map of Eckl (2005). We show that these maps capture interesting geometric properties of $ L$ and use them to analyze abundant divisors.


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Additional Information

Brian Lehmann
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005
Email: blehmann@rice.edu

DOI: https://doi.org/10.1090/S0002-9947-2013-05826-6
Received by editor(s): October 7, 2011
Received by editor(s) in revised form: February 14, 2012
Published electronically: August 15, 2013
Additional Notes: This material is based upon work supported under a National Science Foundation Graduate Research Fellowship.
Article copyright: © Copyright 2013 by the author

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