Zariski decompositions of numerical cycle classes

Fulger, Mihai; Lehmann, Brian

doi:10.1090/jag/677

Authors: Mihai Fulger and Brian Lehmann
Journal: J. Algebraic Geom. 26 (2017), 43-106
DOI: https://doi.org/10.1090/jag/677
Published electronically: August 3, 2016
MathSciNet review: 3570583
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Abstract | References | Additional Information

Abstract: We construct a Zariski decomposition for cycle classes of arbitrary codimension. This decomposition is an analogue of well-known constructions for divisors. Examples illustrate how Zariski decompositions of cycle classes reflect the geometry of the underlying space. We also analyze the birational behavior of Zariski decompositions, leading to a Fujita approximation-type result for curve classes.

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Additional Information

Mihai Fulger
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544 – and – Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700, Bucharest, Romania
Email: afulger@princeton.edu

Brian Lehmann
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005
Address at time of publication: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
MR Author ID: 977848
Email: lehmannb@bc.edu

Received by editor(s): November 26, 2013
Received by editor(s) in revised form: December 7, 2014, and January 5, 2015
Published electronically: August 3, 2016
Additional Notes: The second author was supported by NSF Award 1004363.
Article copyright: © Copyright 2016 University Press, Inc.