# Constructive N\'eron Desingularization of algebras with big smooth locus

## TL;DR

This paper presents an algorithmic proof of the General Néron Desingularization theorem for morphisms with large smooth loci, extending previous one-dimensional results to higher dimensions.

## Contribution

It provides a constructive, algorithmic approach to Néron Desingularization for a broader class of algebraic morphisms.

## Key findings

- Algorithmic proof of the General Néron Desingularization theorem.
- Extension of results from one-dimensional to higher-dimensional cases.
- Uniform version applicable to morphisms with big smooth locus.

## Abstract

An algorithmic proof of the General N\'eron Desingularization theorem and its uniform version is given for morphisms with big smooth locus. This generalizes the results for the one-dimensional case.