Recognizing unstable equidimensional maps, and the number of stable projections of algebraic hypersurfaces

We study the recognition of -classes of multi-germs in families of corank-1 maps from n-space into n-space. From these recognition conditions we deduce certain geometric properties of bifurcation sets of such families of maps. As applications we give a formula for the number of -codimension-1 classes of corank-1 multi-germs from ℂ ⁿ to ℂ ⁿ and an upper bound for the number of stable projections of algebraic hypersurfaces in ℝ ^{n +1} into hyperplanes. Received: 23 July 1998