# Images of analytic map germs, and singular fibrations

## TL;DR

This paper investigates the complex and real analytic map germs with target dimension greater than one, focusing on the phenomena where their images are not well-defined as set germs and local fibrations may not exist, revealing their interrelation.

## Contribution

It characterizes the relationship between the non-well-defined images and the absence of local fibrations for higher-dimensional target map germs.

## Key findings

- The image of the map germ may not be well-defined as a set germ.
- A local fibration near the origin may not exist for these germs.
- The two phenomena are interconnected and can be characterized.

## 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.