Hodge theory meets the minimal model program: a survey of log canonical and Du Bois singularities

TL;DR

This survey explores recent advances in understanding singularities in algebraic geometry, focusing on Du Bois singularities and their relation to the minimal model program.

Contribution

It reviews the definitions, properties, and connections of Du Bois singularities with minimal model program singularities, highlighting recent developments.

Findings

Du Bois singularities have important links to the minimal model program.

Recent progress clarifies the properties and classifications of these singularities.

The survey summarizes key results and open questions in the field.

Abstract

This is a survey of some recent developments in the study of singularities related to the classification theory of algebraic varieties. In particular, the definition and basic properties of Du Bois singularities and their connections to the more commonly known singularities of the minimal model program are reviewed and discussed.