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.
@article{bwmeta1.element.doi-10_1515_coma-2017-0014, author = {Daniele Angella and Cristiano Spotti}, title = {K\"ahler-Einstein metrics: Old and New}, journal = {Complex Manifolds}, volume = {4}, year = {2017}, pages = {200-244}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2017-0014} }
Daniele Angella; Cristiano Spotti. Kähler-Einstein metrics: Old and New. Complex Manifolds, Tome 4 (2017) pp. 200-244. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2017-0014/