Images of analytic map germs, and singular fibrations

Abstract

For a map germ $G$ with target $({\mathbb{C}}^p,0)$ or $({\mathbb{R}}^p,0)$ with $p\ge 2$, we address 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.

revised, to appear in Europ. J. Math