Milnor monodromies and mixed Hodge structures for non-isolated hypersurface singularities

TL;DR

This paper investigates the Milnor monodromies of non-isolated hypersurface singularities, revealing concentration of cohomology in the middle degree for certain eigenvalues and providing explicit formulas for their Jordan normal forms.

Contribution

It offers new insights into the structure of Milnor monodromies for non-isolated singularities and derives explicit formulas for parts of their Jordan normal forms.

Findings

Reduced cohomology groups are concentrated in the middle degree for some eigenvalues.

Explicit formulas for parts of the Jordan normal forms of monodromies.

Enhanced understanding of the monodromy structure in non-isolated hypersurface singularities.

Abstract

We study the Milnor monodromies of non-isolated hypersurface singularities and show that the reduced cohomology groups of the Milnor fibers are concentrated in the middle degree for some eigenvalues of the monodromies. As an application of this result, we give an explicit formula for some parts of their Jordan normal forms.