On the equisingularity class of the general higher order polars of plane branches

TL;DR

This paper investigates the factorization of higher order polar curves of plane branches within their equisingularity class, extending previous results to more general cases.

Contribution

It generalizes existing results on the factorization of higher order polars for plane branches to broader classes within their equisingularity class.

Findings

Describes the factorization of higher order polars for generic plane branches.

Extends previous work by Casas-Alvero and Hefez-Hernandes-Hernández.

Provides a generalized framework for understanding higher order polar curves.

Abstract

In this paper we describe the factorization of the higher order polars of a generic branch in its equisingularity class. We generalize the results of Casas-Alvero and Hefez-Hernandes-Hern\'andez to higher order polars.