# Relative and logarithmic resolution of singularities

## TL;DR

This paper reviews various canonical desingularization methods in characteristic zero, including classical, logarithmic, weighted, and broader context approaches, providing a unified overview of the field.

## Contribution

It offers a comprehensive overview of known desingularization techniques, highlighting recent developments and their applications across different mathematical contexts.

## Key findings

- Summarizes classical and modern desingularization methods.
- Introduces recent logarithmic and weighted desingularization techniques.
- Extends desingularization concepts to wider mathematical settings.

## Abstract

These lecture notes provide a unified overview of most known canonical desingularization methods in characteristic zero. It starts with discussing the classical method, and then proceeds with the recently discovered ones: logarithmic desingularization of logarithmic schemes and morphisms, weighted methods: logarithmic and non-logarithmic ones, desingularization in wider contexts: quasi-excellent schemes and formal schemes, complex and non-archimedean spaces.