Let f : ℂ_n_ —> ℂ be any polynomial function. By using global polar methods, we introduce models for the fibers of f and we study the monodromy at atypical values of f, including the value infinity. We construct a geometric monodromy with controlled behavior and define global relative monodromy with respect to a general linear form. We prove localization results for the relative monodromy and derive a zeta-function formula for the monodromy around an atypical value. We compute the relative zeta function in several cases and emphasize the differences to the “classical” local situation.
Cite this article
Dirk Siersma, Mihai Tibăr, Singularities at Infinity and their Vanishing Cycles, II. Monodromy. Publ. Res. Inst. Math. Sci. 36 (2000), no. 6, pp. 659–679DOI 10.2977/PRIMS/1195139641