On the structure of codimension 1 foliations with pseudoeffective conormal bundle

2014/04/28 by Touzet, Frederic
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.6985

Abstract

Let X a projective manifold equipped with a codimension 1 (maybe singular) distribution whose conormal sheaf is assumed to be pseudoeffective. By a theorem of Jean-Pierre Demailly, this distribution is actually integrable and thus defines a codimension 1 holomorphic foliation \F. We aim at describing the structure of such a foliation, especially in the non abundant case: It turns out that \F is the pull-back of one of the "canonical foliations" on a Hilbert modular variety. This result remains valid for "logarithmic foliated pairs".

Related

• Projectively flat foliations
• Codimension two holomorphic foliations
• On codimension one holomorphic distributions on compact toric orbifolds
• Uniformisation de l'espace des feuilles de certains feuilletages de codimension 1
• Unlikely intersections of codimension one foliations