Zariski invariant for quasi-ordinary hypersurfaces

TL;DR

This paper introduces a new Zariski invariant for quasi-ordinary hypersurfaces, providing a tool to classify and understand surfaces with specific characteristic exponents and moduli.

Contribution

The paper presents a novel $ ilde{ ext{A}}$-invariant for quasi-ordinary parameterizations, advancing the classification of these surfaces with complex moduli.

Findings

Defined a new $ ilde{ ext{A}}$-invariant for quasi-ordinary hypersurfaces

Used the invariant to describe surfaces with one generalized characteristic exponent

Identified conditions for countable moduli in these surfaces

Abstract

We introduced an $\tilde{\mathcal{A}}$-invariant for quasi-ordinary parameterizations and we consider it to describe quasi-ordinary surfaces with one generalized characteristic exponent admitting a countable moduli.