Singularities at Infinity and their Vanishing Cycles, II. Monodromy

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.

Related Papers

• Monodromy at infinity of polynomial maps and Newton polyhedra(2009)
• → Monodromy at Infinity of Polynomial Maps and Newton Polyhedra (with an Appendix by C. Sabbah)(2012)17 cited
• Monodromy at infinity of polynomial maps and mixed Hodge modules(2009)
• → Unfolding polynomial maps at infinity(2000)16 cited
• → Monodromy at infinity of polynomial maps and Newton polyhedra (with Appendix by C. Sabbah)(2009)5 cited