  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.

Algebraic Geometry