# Equimultiplicity of families of map germs from $\mathbb{C}^2$ to $\mathbb{C}^3$

## TL;DR

This paper addresses Zariski's multiplicity conjecture for families of map germs from ^2 to ^3, providing a positive answer for a specific class of non-isolated singularities.

## Contribution

It proves the multiplicity conjecture for a particular class of non-isolated singularities in families of map germs from ^2 to ^3.

## Key findings

- Confirmed Zariski's multiplicity conjecture for certain non-isolated singularities
- Established conditions under which equimultiplicity holds in families
- Contributed to the understanding of singularity behavior in complex mappings

## Abstract

In 1971, Zariski proposed some questions in Theory of Singularities. One of such problems is the so-called, nowadays, Zariski's multiplicity conjecture. In this work, we consider the version of this conjecture for families. We answer positively Zariski's multiplicity conjecture for a special class of non-isolated singularities.