Towards classification of codimension 1 foliations on threefolds of general type

Abstract

We aim to classify codimension 1 foliations $\mathcal{F}$ with canonical singularities and $\nu (K_{\mathcal{F}})<3$ 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 $\mathcal{F}$ with the canonical class $K_{\mathcal{F}}$ being not big on manifolds of general type in any dimension, assuming that $\mathcal{F}$ is non-singular in codimension $2$.

16 pages, further corrections to the statement and proof of Theorem A, final version, to appear in Math. Nachr

References in corpus (3)

• Higher dimensional foliated Mori theory
• Generic positivity and applications to hyperbolicity of moduli spaces
• MMP for co-rank one foliations on threefolds