Images of analytic map germs and singular fibrations

Abstract

For a map germ \(G\) with target \((\bC^{p}, 0)\) or \((\bR^{p}, 0)\) with \(p\ge 2\), we focus on two phenomena which do not occur when \(p=1\): the image of \(G\) may be not well-defined as a set germ, and a local fibration near the origin may not exist. We show how these two phenomena are related, and how they can be characterised.