Classification of absolutely dicritical foliations of cusp type

TL;DR

This paper classifies a specific type of complex plane foliation singularities, called absolutely dicritical of cusp type, based on their topological equivalence to a particular meromorphic function's level set.

Contribution

It provides a comprehensive classification of absolutely dicritical foliations of cusp type, a previously less understood class of singularities.

Findings

Complete topological classification of cusp-type dicritical foliations

Identification of invariants characterizing these singularities

Establishment of normal forms for the classified foliations

Abstract

We give a classification of absolutely dicritical foliations of cusp type, that is, the germ of singularities of complex foliations in the complex plane topologically equivalent to the singularity given by the level of the meromorphic function \frac{y^{2}+x^{3}}{xy}.