Interaction Between Singularity Theory and the Minimal Model Program

TL;DR

This paper surveys recent developments connecting singularity theory with the minimal model program, including dual complexes, the ACC conjecture, and local stability of Kawamata log terminal singularities.

Contribution

It provides an overview of recent progress in understanding singularities within the minimal model program, highlighting new proofs and theories.

Findings

Proof of the ACC conjecture for log canonical thresholds

Construction and properties of dual complexes

Advances in local stability theory of Kawamata log terminal singularities

Abstract

We survey some recent topics on singularities, with a focus on their connection to the minimal model program. This includes the construction and properties of dual complexes, the proof of the ACC conjecture for log canonical thresholds and the recent progress on the `local stability theory' of an arbitrary Kawamata log terminal singularity.