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

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.