Analytic classification of a class of cuspidal foliations in $({\mathbb C}^3,0)$

TL;DR

This paper provides an analytic classification for a specific class of cuspidal holomorphic foliations in three-dimensional complex space, using the concept of essential holonomy from singularity reduction.

Contribution

It introduces a new classification method based on essential holonomy for quasi-homogeneous cuspidal foliations in ^3, extending understanding of their local structure.

Findings

Classification achieved via essential holonomy

Applicable to quasi-homogeneous cuspidal foliations

Advances in singularity reduction techniques

Abstract

In this article we study the analytic classification of certain types of quasi-homogeneous cuspidal holomorphic foliations in $(\CC^3,{\bf 0})$ via the essential holonomy defined over one of the components of the exceptional divisor that appears in the reduction of the singularities of the foliation.