Positive Rational Nodal Leaves on Surfaces

TL;DR

This paper classifies certain singular holomorphic foliations on compact complex surfaces that contain an invariant rational nodal curve with positive self-intersection, under specific assumptions.

Contribution

It provides a complete list of possible foliations with these properties, advancing the understanding of their structure and classification.

Findings

List of all possible foliations under given conditions

Identification of constraints imposed by the invariant rational nodal curve

Enhanced classification framework for foliations on complex surfaces

Abstract

We consider singular holomorphic foliations on compact complex surfaces with invariant rational nodal curve of positive self-intersection. Then, under some assumptions, we list all possible foliations.