K\"ahler-Einstein metrics: Old and New
Daniele Angella, Cristiano Spotti
TL;DR
This paper reviews classical and recent developments in the theory of K"ahler-Einstein metrics on compact complex manifolds, emphasizing existence criteria, obstructions, and links to algebraic stability concepts.
Contribution
It summarizes key results and connections between K"ahler-Einstein metrics and algebraic stability, serving as educational notes rather than original research.
Findings
Overview of existence and obstruction results
Discussion of stability conditions like K-stability
Connections between differential geometry and algebraic geometry
Abstract
We present classical and recent results on K\"ahler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI course "K\"ahler-Einstein metrics" given by C.S. in Cortona (Italy), May 2017. The material is not intended to be original.
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