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Kähler–Einstein metrics on Fano manifolds

  • Special Feature: The Takagi Lectures
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Japanese Journal of Mathematics Aims and scope

Abstract

This is an expository paper on Kähler metrics of positive scalar curvature. It is for my Takagi Lectures at RIMS in November of 2013. In this paper, I first discuss the Futaki invariants, the K-stability and its relation to the K-energy. Next I will outline my work in 2012 on the existence of Kähler–Einstein metrics on K-stable Fano manifolds. Finally, I will present S. Paul’s work on stability of pairs with some modifications of mine.

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Authors and Affiliations

  1. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, P.R. China

    Gang Tian

  2. Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    Gang Tian

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  1. Gang Tian
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Correspondence to Gang Tian.

Additional information

Communicated by: Hiraku Nakajima

This article is based on the 13th Takagi Lectures that the author delivered at Research Institute for Mathematical Sciences, Kyoto University on November 16 and 17, 2013.

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Tian, G. Kähler–Einstein metrics on Fano manifolds. Jpn. J. Math. 10, 1–41 (2015). https://doi.org/10.1007/s11537-014-1387-3

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  • DOI: https://doi.org/10.1007/s11537-014-1387-3

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