Orthogonality of divisorial Zariski decompositions for classes with volume zero

TL;DR

This paper proves that the orthogonality conjecture for divisorial Zariski decompositions is valid for pseudoeffective (1,1) classes with zero volume on compact Kähler manifolds, advancing understanding in complex geometry.

Contribution

It establishes the orthogonality conjecture specifically for classes with zero volume, filling a gap in the theory of Zariski decompositions.

Findings

Orthogonality conjecture holds for volume zero classes.

Advances understanding of divisorial Zariski decompositions.

Provides new insights into pseudoeffective classes on Kähler manifolds.

Abstract

We show that the orthogonality conjecture for divisorial Zariski decompositions on compact Kahler manifolds holds for pseudoeffective (1,1) classes with volume zero.