Kodai Mathematical Journal

Bifurcation set, M-tameness, asymptotic critical values and Newton polyhedrons

Tat Thang Nguyen

Full-text: Open access


Let F = (F1, F2, ..., Fm): CnCm be a polynomial dominant mapping with n > m. In this paper we give the relations between the bifurcation set of F and the set of values where F is not M-tame as well as the set of generalized critical values of F. We also construct explicitly a proper subset of Cm in terms of the Newton polyhedrons of F1, F2, ..., Fm and show that it contains the bifurcation set of F. In the case m = n – 1 we show that F is a locally C-trivial fibration if and only if it is a locally C0-trivial fibration.

Article information

Kodai Math. J., Volume 36, Number 1 (2013), 77-90.

First available in Project Euclid: 29 March 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Nguyen, Tat Thang. Bifurcation set, M-tameness, asymptotic critical values and Newton polyhedrons. Kodai Math. J. 36 (2013), no. 1, 77--90. doi:10.2996/kmj/1364562720. https://projecteuclid.org/euclid.kmj/1364562720

Export citation