manuscripta mathematica

, Volume 110, Issue 2, pp 145–157

On the generalized critical values of a polynomial mapping

  • Zbigniew Jelonek

DOI: 10.1007/s00229-002-0320-x

Cite this article as:
Jelonek, Z. Manuscripta Math. (2003) 110: 145. doi:10.1007/s00229-002-0320-x


 Let \(\) be a polynomial dominant mapping and let deg fid. 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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Zbigniew Jelonek
    • 1
  1. 1.Instytut Matematyczny, Polska Akademia Nauk, Św. Tomasza 30, 31-027 Kraków, Poland. e-mail: