Recognizing unstable equidimensional maps, and the number of stable projections of algebraic hypersurfaces
A smooth \(({\mathcal C}^\infty\) or analytic) map is unstable if it has positive \({\mathcal A}_e\)-codimension as an \(s\)-germ for some set of source points \(x_1,x_2, \dots, x_s\). The author studies the recognition of unstable maps in families \(F\) of equidimensional corank-1 maps, both in the local situation where \(F\) is an unfolding germ and in the global situation where \(F\) is the restriction of the family of all (central or parallel) projections into hyperplates to a smooth hypersurface given as the zero-set of some smooth function. Using these recognition conditions, he deduces certain local and global properties of the bifurcation set \({\mathcal B}\) in the parameter space of \(F\).
scientific article; zbMATH DE number 1310199