Join operation and $\mathcal{A}$-finite map-germs

Abstract

In this work we define some map-germs, called elementary joins, for the purpose of producing new $\mathcal{A}$-finite map-germs from them. In particular, we describe a general form of an $\mathcal{A}$-finite monomial map from $({\mathbb{C}}^n,0)$ to $({\mathbb{C}}^p,0)$ for $p\ge 2n$ of any corank in terms of elementary join maps. Our main tools are the delta invariant and some invariants of curves.

18 pages