Divisorial Zariski Decomposition and some properties of full mass currents

TL;DR

This paper characterizes the divisorial Zariski decomposition of a big class on a compact Kähler manifold via volume equality and explores related properties of full mass currents.

Contribution

It provides a new criterion for the divisorial Zariski decomposition based on volume comparison and derives properties of full mass currents from this characterization.

Findings

Characterization of divisorial Zariski decomposition through volume equality.

Establishment of properties of full mass currents.

Insight into the structure of big classes on Kähler manifolds.

Abstract

Let $\alpha$ be a big class on a compact K\"ahler manifold. We prove that a decomposition $\alpha=\alpha_1+\alpha_2$ into the sum of a modified nef class $\alpha_1$ and a pseudoeffective class $\alpha_2$ is the divisorial Zariski decomposition of $\alpha$ if and only if $\operatorname{vol}(\alpha)=\operatorname{vol}(\alpha_1)$. We deduce from this result some properties of full mass currents.