On the simplicity of multigerms

TL;DR

This paper investigates the simplicity of multigerms through various operations, providing classifications and results especially for multigerms from complex three-dimensional spaces.

Contribution

It introduces new results on the simplicity of multigerms, including classifications for those from a23 to a23, and explores cases involving non-stable primitive germs.

Findings

Classification of all simple multigerms from a23 to a23

Results on multigerms obtained via augmentation and concatenation

Identification of cases with non-stable primitive germs

Abstract

We prove several results regarding the simplicity of germs and multigerms obtained via the operations of augmentation, simultaneous augmentation and concatenation and generalised concatenation. We also give some results in the case where one of the branches is a non stable primitive germ. Using our results we obtain a list which includes all simple multigerms from $\mathbb C^3$ to $\mathbb C^3$.