@article{7dbbc190c705473b91da53c5f2d7053d,
title = "K{\"a}hler-Einstein metrics on Fano surfaces",
abstract = "We give an exposition of a result of G. Tian, which says that a Fano surface admits a K{\"a}hler-Einstein metric precisely when the Lie algebra of holomorphic vector fields is reductive.",
keywords = "Fano surfaces, K{\"a}hler-Einstein metrics",
author = "Valentino Tosatti",
note = "Funding Information: I am grateful to Z. Lu, R. Seyyedali, J. Song, G. Sz{\'e}kelyhidi and B. Weinkove for very useful comments, and to D.H. Phong for encouragement. I am also grateful to the referee for very useful remarks and suggestions. These notes were originally written for my talks at the Informal Complex Geometry and PDE seminar at Columbia University in December 2009. I wish to thank all the participants in the seminar. This work was partially supported by National Science Foundation grant DMS-1005457 . ",
year = "2012",
doi = "10.1016/j.exmath.2011.07.003",
language = "English (US)",
volume = "30",
pages = "11--31",
journal = "Expositiones Mathematicae",
issn = "0723-0869",
publisher = "Elsevier GmbH",
number = "1",
}