Homotopy groups of generic leaves of logarithmic foliations

TL;DR

This paper investigates the homotopy groups of generic leaves in logarithmic foliations on complex projective manifolds, revealing a relationship with the complement of the polar divisor.

Contribution

It establishes a connection between the homotopy groups of generic leaves and the complement of the polar divisor in logarithmic foliations.

Findings

Homotopy groups of generic leaves are related to the complement of the polar divisor.

Provides new insights into the topology of logarithmic foliations.

Establishes a formula linking homotopy groups of leaves and divisors.

Abstract

We study the homotopy groups of generic leaves of logarithmic foliations on complex projective manifolds. We exhibit a relation between the homotopy groups of a generic leaf and of the complement of the polar divisor of the logarithmic foliation.