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

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• Let F = (F1, F2, ..., Fm): Cn → Cm 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.

• 国立大学法人 東京工業大学大学院理工学研究科数学専攻の論文

国立大学法人 東京工業大学大学院理工学研究科数学専攻 | 論文

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