Monodromy zeta-function of a polynomial on a complete intersection and Newton polyhedra

TL;DR

This paper derives explicit formulas for the monodromy zeta-function of a polynomial on a complete intersection using Newton polyhedra, extending known results to a broader class of deformations.

Contribution

It provides new explicit formulas for the monodromy zeta-function in terms of Newton polyhedra for non-degenerate deformations of complete intersections.

Findings

Explicit formulas for monodromy zeta-function in terms of Newton polyhedra

Extension of Libgober--Sperber theorem to complete intersections

Applicable to non-degenerate polynomial deformations

Abstract

For a generic (polynomial) one-parameter deformation of a complete intersection, there is defined its monodromy zeta-function. We provide explicit formulae for this zeta-function in terms of the corresponding Newton polyhedra in the case the deformation is non-degenerate with respect to its Newton polyhedra. Using this result we obtain the formula for the monodromy zeta-function at the origin of a polynomial on a complete intersection, which is an analog of the Libgober--Sperber theorem.