Let X ⊂ C n be an affine variety and f : X → C m be the restriction to X of a polynomial map C n → C m. We construct an affine Whitney stratification of X. The set K (f) of stratified generalized critical values of f can also be computed. We show that K (f) is a nowhere dense subset of C m which contains the set B(f) of bifurcation values of f by proving a version of the Thom isotopy lemma for nonproper polynomial maps on singular varieties.

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