Let be a nonsingular algebraic set and be a polynomial function. It is well known that the restriction of on is a locally trivial fibration outside a finite set In this paper we give an explicit description of a finite set such that where denotes the set of critical values of the Furthermore, is contained in the set of critical values of certain polynomial functions provided that the is Newton nondegenerate at infinity. Using these facts, we show that if is a family of polynomials such that the Newton polyhedron at infinity of is independent of and the is Newton nondegenerate at infinity, then the global monodromies of the are all isomorphic.
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Tat Thang Nguyen, Phú Phát Phạm, Tiến-Sơn Phạm, Bifurcation Sets and Global Monodromies of Newton Nondegenerate Polynomials on Algebraic Sets. Publ. Res. Inst. Math. Sci. 55 (2019), no. 4, pp. 811–834DOI 10.4171/PRIMS/55-4-6