For a map germ G with target (C p , 0) or (R p , 0) with p ≥ 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.
Abstract. In more than two variables, detection of the bifurcation set of polynomial mapping R n → R p , n ≥ p, is a still unsolved problem. In this note we provide a solution for n = p + 1 ≥ 3.
In this paper we give an example of a bounded Stein domain in C n , with smooth boundary, which is not Runge and whose intersection with every complex line is simply connected.
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