Singularities at infinity and their vanishing cycles, II : monodromy

Abstract

Let f C n C be any polynomial function By using global polar methods we introduce models for the bers of f and we study the monodromy at atypical values of f including the value innity We construct a geometric monodromy with controlled behavior and dene global relative monodromy with respect to a general linear form We prove localization results for the relative monodromy and derive a zetafunction formula for the monodromy around an atypical value We compute the relative zeta function in several cases and emphasize the dierences to the classical local situation