Smooth and singular Kahler-Einstein metrics

TL;DR

This paper surveys recent developments in the study of singular Kahler-Einstein metrics, highlighting their importance in understanding smooth metrics and their applications in differential and algebraic geometry.

Contribution

It provides a comprehensive overview of the progress in singular Kahler-Einstein metrics, emphasizing their intrinsic interest and utility in geometric research.

Findings

Singular Kahler-Einstein metrics are crucial in understanding smooth metrics.

Recent advances have expanded the applications of singular metrics in geometry.

The survey summarizes key developments over the past decades.

Abstract

Smooth Kahler-Einstein metrics have been studied for the past 80 years. More recently, singular Kahler-Einstein metrics have emerged as objects of intrinsic interest, both in differential and algebraic geometry, as well as a powerful tool in better understanding their smooth counterparts. This article is mostly a survey of some of these developments.