Kähler-Einstein metrics: Old and New

Abstract

We present classical and recent results on Kähler-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 "Kähler-Einstein metrics" given by C.S. in Cortona (Italy), May 2017. The material is not intended to be original.

Keywords

• kähler-einstein
• fano
• k-stability
• yau-tian-donaldson conjecture
• moduli of kähler-einstein
• 53c55