On the 1- adjoint canonical divisor of a foliation

Abstract

In this paper, we describe the structure of the negative part of a Zariski decomposition of \(K_X+K_{{{\mathcal {F}}}}\) for a relatively minimal foliation \((X,{{\mathcal {F}}})\) whenever \(K_X+K_{{{\mathcal {F}}}}\) is pseudoeffective.