Projectively flat foliations

2024/01/06 by Stéphane Druel, Druel, Stéphane
Mathematics · #14E20 #14E30 #32Q26 #32Q30 #37F75 #53B10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2401.03311

openalex publication_date 2024/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the structure of regular codimension 1 foliations with numerically projectively flat tangent bundle on complex projective manifolds of dimension at least 4. Along the way, we prove that either the normal bundle of a regular codimension 1 foliation is pseudo-effective, or its conormal bundle is nef.

Related

• Singular foliations with trivial canonical class
• Compact leaves of codimension one holomorphic foliations on projective\n manifolds
• On foliations with nef anti-canonical bundle
• Codimension one regular foliations on rationally connected threefolds
• On the structure of codimension 1 foliations with pseudoeffective conormal bundle