Current Developments in Mathematics

Volume 2015

Kähler–Einstein metrics and algebraic geometry

Pages: 1 – 25



Simon Donaldson (Imperial College, London, United Kingdom; and Simons Centre for Geometry and Physics, Stony Brook, New York, U.S.A.)


This paper is a survey of some recent developments in the area described by the title, and follows the lines of the author’s lecture in the 2015 Harvard Current Developments in Mathematics meeting. The main focus of the paper is on the Yau conjecture relating the existence of Kähler–Einstein metrics on Fano manifolds to K-stability. We discuss four different proofs of this, by different authors, which have appeared over the past few years. These involve an interesting variety of approaches and draw on techniques from different fields.

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