Milnor fibers over singular toric varieties and nearby cycle sheaves

Abstract

We propose a new sheaf-theoretical method for the calculation of the monodromy zeta functions of Milnor fibrations. As an application, classical formulas of Kushnirenko and Varchenko etc. concerning polynomials on $\CC^n$ will be generalized to polynomial functions on any toric variety.

arXiv comment28pages; Chapter 4 of the previous version of "A geometric degree formula for $A$-discriminants and Euler obstructions of toric varieties" (arXiv:0807.3163) became an independent paper; Revised

References in corpus (2)

• Combinatorial aspects of the mixed Hodge structure
• Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves

Cited by in corpus (8)

• Determinantal singularities and Newton polyhedra
• Newton polyhedra of discriminants of projections
• Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves
• Coefficients of the poles of local zeta functions and their applications to oscillating integrals
• Multivariate Abel-Ruffini
• Motivic Milnor fibers over complete intersection varieties and their virtual Betti numbers
• A geometric degree formula for $A$-discriminants and Euler obstructions of toric varieties
• Monodromy at infinity of $A$-hypergeometric functions and toric compactifications