# Holomorphic foliations tangent to Levi-flat subsets

## TL;DR

This paper investigates the properties of Segre varieties linked to Levi-flat subsets in complex manifolds and uses them to derive new local and global results on integrating tangent holomorphic foliations.

## Contribution

It introduces novel methods involving Segre varieties to analyze Levi-flat subsets and their associated holomorphic foliations, advancing understanding of their structure and integrability.

## Key findings

- Established new local integrability conditions for tangent holomorphic foliations.
- Derived global results on the structure of Levi-flat subsets.
- Connected Segre varieties to foliation properties in complex manifolds.

## Abstract

We study Segre varieties associated to Levi-flat subsets in complex manifolds and apply them to establish local and global results on the integration of tangent holomorphic foliations.