Compact leaves of codimension one holomorphic foliations on projective manifolds

TL;DR

This paper investigates the structure of codimension one holomorphic foliations on projective manifolds with a focus on compact leaves, exploring their normal bundle properties, holonomy dynamics, and classification results.

Contribution

It introduces new results linking the flatness of the normal bundle and holonomy representations to the global structure of such foliations.

Findings

Existence conditions for foliations with specific compact leaves

Classification of foliations with abelian or solvable holonomy

Factorization results for foliations with compact leaves

Abstract

This article studies codimension one foliations on projective man-ifolds having a compact leaf (free of singularities). It explores the interplay between Ueda theory (order of flatness of the normal bundle) and the holo-nomy representation (dynamics of the foliation in the transverse direction). We address in particular the following problems: existence of foliation having as a leaf a given hypersurface with topologically torsion normal bundle, global structure of foliations having a compact leaf whose holonomy is abelian (resp. solvable), and factorization results.