Towards classification of codimension 1 foliations on threefolds of\n general type

2021/03/03 by Aleksei Golota, Golota, Aleksei
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2103.02780

openalex publication_date 2021/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We aim to classify codimension 1 foliations mathscrF with canonical\nsingularities and \ν(K_ mathscrF) < 3 on threefolds of general type. We\nprove a classification result for foliations satisfying these conditions and\nhaving non-trivial algebraic part. We also describe purely transcendental\nfoliations mathscrF with the canonical class K_ mathscrF being not\nbig on manifolds of general type in any dimension, assuming that mathscrF\nis non-singular in codimension 2.\n

Citations

• Generic positivity and applications to hyperbolicity of moduli spaces
• Higher-dimensional foliated Mori theory

Related

• Codimension one foliations with trivial canonical class on singular spaces II
• Singular foliations with trivial canonical class
• Codimension 1 foliations with numerically trivial canonical class on singular spaces
• Codimension one foliations of degree three on projective spaces
• Codimension one regular foliations on rationally connected threefolds