We prove that a map germ f:(Cn,S)→(Cn+1,0) with
isolated instability is stable if and only if μI(f)=0, where μI(f) is
the image Milnor number defined by Mond. In a previous paper we proved this
result with the additional assumption that f has corank one. The proof here
is also valid for corank ≥2, provided that (n,n+1) are nice dimensions
in Mather's sense (so μI(f) is well defined). Our result can be seen as a
weak version of a conjecture by Mond, which says that the
Ae-codimension of f is ≤μI(f), with equality if f is
weighted homogeneous. As an application, we deduce that the bifurcation set of
a versal unfolding of f is a hypersurface.Comment: 18 pages, 5 figure