Motivic Milnor fibers over complete intersection varieties and their virtual Betti numbers

TL;DR

This paper investigates the monodromy of complete intersection varieties using motivic Milnor fibers, linking their properties to mixed volumes of Newton polyhedron faces for explicit descriptions.

Contribution

It introduces a new approach connecting motivic Milnor fibers with mixed volumes of Newton polyhedra faces to analyze monodromy.

Findings

Explicit descriptions of Jordan normal forms of monodromies

Connection between motivic Milnor fibers and mixed volumes

Application to complete intersection subvarieties

Abstract

We study the Jordan normal forms of the local and global monodromies over complete intersection subvarieties of $C^n$ by using the theory of motivic Milnor fibers. The results will be explicitly described by the mixed volumes of the faces of Newton polyhedrons.