Restricted volumes and divisorial Zariski decompositions

Abstract

We give a relation between the existence of a Zariski decomposition and the behavior of the restricted volume of a big divisor on a smooth (complex) projective variety. Moreover, we give an analytic description of the restricted volume in the line of Boucksom's work. It enables us to define the restricted volume of a transcendental class on a compact Kähler manifold in natural way. The relation can be extended to a transcendental class.

24 pages, to appear in Amer. J. Math, v2: completely revised

References in corpus (3)

• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• Monge-Ampère equations in big cohomology classes
• Bertini Type Theorems

Cited by in corpus (1)

• Properties of Caratheodory measure hyperbolic universal covers of compact Kahler manifolds