Plane branches with Newton nondegenerate polars

TL;DR

This paper characterizes the equisingularity classes of irreducible plane curve germs with Newton nondegenerate general polars, providing explicit Zariski open sets and describing their topology.

Contribution

It offers a detailed characterization of equisingularity classes with Newton nondegenerate polars and constructs explicit open sets with topological descriptions.

Findings

Identifies conditions for Newton nondegeneracy in general polars.

Provides explicit Zariski open sets within equisingularity classes.

Describes the topology of curves with Newton nondegenerate polars.

Abstract

We characterize the equisingularity classes of irreducible plane curve germs whose general members have a Newton nondegenerate general polar curve. In addition, we give explicit Zariski open sets of curves in such equisingularity classes whose general polars are Newton nondegenerate and describe their topology.