Dynamical aspects of foliations with ample normal bundle

Abstract

We prove the following result that was conjectured by Brunella: Let X be a compact complex manifold of dimension ≥ 3. Let F be a codimension one holomorphic foliation on X with ample normal bundle. Then every leaf of F accumulates to the singular set of F .

A brief survey on residue theory of holomorphic foliations

“…The Theorem 3.6 is a partial answer to Brunella's conjecture, see ([13], Conjecture 1.1, p.3102), in the special case when Pic(X) = Z. Recently, in 2021 M. Adachi and J. Brinkschulte have proved the Brunella's conjecture without hypotheses on manifold X , see ( [1], Main Theorem, p.1). Theorem 3.7.…”

“…In 1984, T. Suwa in [48] considers a foliation of complete intersection type and express a certain class of residues in terms of the Chern classes and the local Chern classes of the sheaf Ext 1 O M (Ω F , O M ). As an application, in 3.8 Corollary he gives a partial answer to Rationality Conjecture (see [7], p. 287).…”