# Examples of finitely determined map-germs of corank 3 supporting Mond's $\mu \geq \tau$-type conjecture

## TL;DR

This paper presents the first examples of finitely determined corank 3 map-germs from 3-space to 4-space, supporting Mond's conjecture relating the image Milnor number and $ ext{A}_e$-codimension.

## Contribution

It provides the first known examples of such map-germs and demonstrates their support for Mond's $ ext{μ}
geq au$-type conjecture.

## Key findings

- Support for Mond's conjecture in specific corank 3 cases
- First examples of finitely determined map-germs from 3-space to 4-space
- Validation of the conjecture's inequality in these examples

## Abstract

We give the first examples of finitely determined map-germs of corank 3 defined from 3-space to 4-space. We show that they support Mond's conjecture which states that the image Milnor number is greater than or equal to $\mathcal{A}_e$-codimension for a finitely determined map-germ from $n$-space to $(n+1)$-space (with equality for weighted homogeneous case).