Monodromy at infinity of polynomial maps and Newton polyhedra (with Appendix by C. Sabbah)

TL;DR

This paper introduces motivic Milnor fibers at infinity for polynomial maps, linking monodromy nilpotent parts to Newton polyhedra at infinity, offering new methods to analyze monodromies at infinity.

Contribution

It proposes a novel approach using motivic Milnor fibers at infinity to study monodromy nilpotent parts and relates Jordan block counts to Newton polyhedra at infinity.

Findings

Jordan block counts are described by Newton polyhedra at infinity.

Motivic Milnor fibers at infinity provide new tools for monodromy analysis.

Methods connect geometric properties of polynomials with monodromy behavior.

Abstract

By introducing motivic Milnor fibers at infinity of polynomial maps, we propose some methods for the study of nilpotent parts of monodromies at infinity. The numbers of Jordan blocks in the monodromy at infinity will be described by the Newton polyhedron at infinity of the polynomial.