Monodromy zeta-functions of deformations and Newton diagrams

TL;DR

This paper derives a Varchenko type formula for the monodromy zeta-function of non-degenerate deformations of complex analytic functions, linking it to Newton diagrams.

Contribution

It provides a new explicit formula for the monodromy zeta-function in the context of deformations non-degenerate with respect to Newton diagrams.

Findings

Varchenko type formula established for monodromy zeta-functions

Formula applies to non-degenerate deformations

Connects monodromy zeta-functions with Newton diagrams

Abstract

For a one-parameter deformation of an analytic complex function germ of several variables, there is defined its monodromy zeta-function. We give a Varchenko type formula for this zeta-function if the deformation is non-degenerate with respect to its Newton diagram.