The embedded Nash problem in singular spaces: the case of surfaces

TL;DR

This paper extends the embedded Nash problem to singular ambient spaces and provides a solution specifically for surfaces, broadening the understanding of singularity resolution in algebraic geometry.

Contribution

It generalizes the embedded Nash problem to include singular ambient spaces and solves it for the case of surfaces, advancing the theory of singularities.

Findings

Solved the embedded Nash problem for surfaces with singular ambient spaces

Generalized previous results to a broader class of singularities

Contributed to the understanding of singularity resolution in algebraic geometry

Abstract

We introduce the embedded Nash problem allowing singularities in the ambient space, and solve it in the case of surfaces, generalizing \cite[Theorem 1.22]{BdlB}.