Bijectiveness of the Nash Map for Quasi-Ordinary Hypersurface Singularities

TL;DR

This paper proves that the Nash map is bijective for quasi-ordinary hypersurface singularities, confirming a conjecture for this class and extending previous results to a broader context.

Contribution

It establishes the bijectiveness of the Nash map specifically for quasi-ordinary hypersurface singularities, advancing understanding of arc spaces in singularity theory.

Findings

Confirmed Nash's conjecture for quasi-ordinary hypersurface singularities

Extended previous techniques to a new class of singularities

Provided a positive answer to a longstanding question in algebraic geometry

Abstract

In this paper we give a positive answer to a question of Nash concerning the arc space of a singularity, for the class of quasi-ordinary hypersurface singularities, extending to this case previous results and techniques of Shihoko Ishii.