Divisorial Zariski decomposition and some properties of full mass currents

Abstract

Letbe a big class on a compact Kahler manifold. We prove that a decomposition � = �1 +�2 into the sum of a modified nef class �1 and a pseudoeffective class �2 is the divisorial Zariski decomposition ofif and only if vol(�) = vol(�1). We deduce from this result some properties of full mass currents.