Monodromy of plane curves and quasi-ordinary surfaces

TL;DR

This paper introduces recursive formulas for the monodromies of quasi-ordinary surfaces, revealing a novel approach to understanding the monodromy of Milnor fibrations in plane curve singularities.

Contribution

It develops recursive formulas for monodromies of quasi-ordinary surfaces and uncovers a new method to express monodromy of plane curve Milnor fibrations.

Findings

Recursive formulas for monodromies of quasi-ordinary surfaces

New expression for monodromy of plane curve Milnor fibrations

Enhanced understanding of surface singularity monodromies

Abstract

We develop recursive formulas for the horizontal and vertical monodromies of a quasi-ordinary surface. These are monodromies associated to the Milnor fiber of a slice transverse to a component of the singular locus. In the course of working out these recursions, we have discovered what appears to be a new way to express the monodromy associated to the Milnor fibration of a singular plane curve.