Resolution Algorithms and Deformations

TL;DR

This paper presents a resolution algorithm for singularities in characteristic zero using multi-ideals, aiming for applications in simultaneous resolution of singularities, especially for parametrized families.

Contribution

It introduces a new resolution algorithm based on multi-ideals, simplifying the process and enhancing potential for applications in families parametrized by artinian rings.

Findings

The algorithm effectively resolves singularities in characteristic zero.

Multi-ideals provide a simple and suitable framework for resolution.

Potential for applications in simultaneous resolution of singularities.

Abstract

An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a finite sequence of pairs, each one consiting of a sheaf of ideals and a positive integer. This approach is particularly simple and, as indicated by some results shown here, it seems suitable for applications to a good theory of simultaneous algorithmic resolution of singularities, specially for families parametrized by the spectrum of an artinian ring.