Bifurcation of plane-to-plane map-germs with corank two of parabolic type

TL;DR

This paper analyzes the bifurcation behavior of specific plane-to-plane map-germs with corank two, providing explicit descriptions of their unfolding and applications to parabolic geometric objects.

Contribution

It explicitly describes the bifurcation diagram of A-versal unfoldings for corank two plane-to-plane germs of parabolic type, a novel contribution to singularity theory.

Findings

Explicit bifurcation diagram of A-versal unfolding

Applications to parabolic geometric objects

Classification of corank two map-germs

Abstract

We study a moduli stratum of A-orbits of plane-to-plane germs of corank 2 with codimension 3. We describe explicitly the bifurcation diagram of its topologically A-versal unfolding. Two geometric applications to parabolic objects are presented.