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

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.