Singularities at Infinity and their Vanishing Cycles, II. Monodromy
Publications of the Research Institute for Mathematical Sciences2000Vol. 36(6), pp. 659–679
Citations Over TimeTop 25% of 2000 papers
Abstract
Let f : ℂ^n \to 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.
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