Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves

TL;DR

This paper extends the understanding of monodromy zeta functions at infinity for polynomial maps by employing sheaf-theoretical methods, providing new formulas for global monodromy along bifurcation fibers.

Contribution

It introduces a sheaf-theoretical framework to generalize existing formulas for monodromy zeta functions at infinity, applicable to various polynomial map directions.

Findings

Derived new formulas for monodromy zeta functions at infinity

Extended Libgober-Sperber formula to broader contexts

Provided formulas for monodromy along bifurcation fibers

Abstract

By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained.