On the classification of quasi-homogeneous curves

TL;DR

This paper uses holomorphic foliation techniques to analyze quasi-homogeneous curves in complex two-space, providing a practical method to determine their analytic equivalence.

Contribution

It introduces an effective technique based on holomorphic foliations to classify quasi-homogeneous curves analytically.

Findings

Developed a method to distinguish quasi-homogeneous curves analytically.

Connected holomorphic foliation invariants with curve classification.

Provided criteria for analytic equivalence of quasi-homogeneous curves.

Abstract

We apply techniques of Holomorphic Foliations in the description of the analytic invariants associated to germs of quasi-homogeneous curves in $(\mathbb{C}^2,0)$. As a consequence we obtain an effective method to determine whether two quasi-homogeneous curves are analytically equivalent.