Towards classification of codimension 1 foliations on threefolds of general type

Abstract

We aim to classify codimension 1 foliations F with canonical singularities and ν(K F ) < 3 on threefolds of general type. We prove a classification result for foliations satisfying these conditions and having non-trivial 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 non-singular in codimension 2.