Zariski decompositions of numerical cycle classes
arXiv:1310.0538
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.
50 pages, 1 figure; v2: updated references; v3: minor corrections