Toward classification of codimension 1 foliations on threefolds of general type

Abstract

The aim of this paper is to classify codimension 1 foliations ℱ with canonical singularities and 𝜈(𝐾 ℱ ) < 3 on threefolds of general type. I prove a classification result for foliations satisfying these conditions and having nontrivial algebraic part. We also describe purely transcendental foliations ℱ with the canonical class 𝐾 ℱ being not big on manifolds of general type in any dimension, assuming that ℱ is nonsingular in codimension 2.