A note on 1-parameter stable unfoldings

Abstract

We give two characterisations of when a map-germ admits a 1-parameter stable unfolding, one related to the ${\mathcal{K}}_e$-codimension and another related to the normal form of a versal unfolding. We then prove that there are infinitely many finitely determined map-germs of multiplicity 4 from ${\mathbb{K}}^3$ to ${\mathbb{K}}^3$ which do not admit a 1-parameter stable unfolding.