Images of maps from $({\mathbb{C}}^2,0)$ to $({\mathbb{C}}^n,0)$

Abstract

Let $F:({\mathbb{C}}^2,0)\to ({\mathbb{C}}^n,0)$ be the germ of a finite map and $(X,0)$ be its image. We will in this article using the topology of the link show that $(X,0)$ has to be a quotient singularity if it is normal and describe the possible topological types. Including a discussion of the groups and examples of how to construct a map to a given topology. We will also discuss the case when the image is not normal.

21 Pages