Topology of leaves of generic logarithmic foliations on $\mathbb{CP}^2$

TL;DR

This paper classifies the topological types of leaves in generic logarithmic foliations on the complex projective plane, showing most are biholomorphic to  or homeomorphic to the Loch Ness monster surface.

Contribution

It provides a complete topological classification of leaves in these foliations, identifying their biholomorphic and homeomorphic types.

Findings

Most leaves are biholomorphic to 

Remaining leaves are homeomorphic to the Loch Ness monster surface

Only finitely many leaves are exceptions

Abstract

We describe the topological types of leaves of generic logarithmic foliations on the complex projective plane. We prove that all leaves, except for a finite many are biholomorphic to $\mathbb{C}$ or homeomorphic to the surface known as Loch Ness monster.