Curvature criteria of A-simple singularities R,0-> R^2,0 and their parallel curves

TL;DR

This paper introduces curvature parameters for singular plane curves with finite multiplicities, establishes criteria for their A-simple singularity types, and explores the singularity types of their parallel curves.

Contribution

It defines curvature parameters for singular curves and provides new criteria for classifying their A-simple singularities and analyzing parallel curves.

Findings

Criteria for A-simple singularity classification

Curvature parameters for singular plane curves

Analysis of singularity types of parallel curves

Abstract

We introduce the notion of curvature parameters for singular plane curves with finite multiplicities and define the notion of curvatures for them. We then provide criteria to determine their singularity types for A-simple singularities. As an application, we investigate singularity types of their parallel curves.