On the generalized critical values of a polynomial mapping

Abstract

 Let be a polynomial dominant mapping and let deg f _i ≤d. We prove that the set K(f) of generalized critical values of f is contained in the algebraic hypersurface of degree at most D=(d+s(m−1)(d−1))ⁿ, where . This implies in particular that the set B(f) of bifurcations points of f is contained in the hypersurface of degree at most D=(d+s(m−1)(d−1))ⁿ. We give also an algorithm to compute the set K(f) effectively.