Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof

Chen, Xiuxiong; Donaldson, Simon; Sun, Song

doi:10.1090/S0894-0347-2014-00801-8

Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath$2\pi$ and completion of the main proof
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by Xiuxiong Chen, Simon Donaldson and Song Sun

J. Amer. Math. Soc. 28 (2015), 235-278

DOI: https://doi.org/10.1090/S0894-0347-2014-00801-8

Published electronically: March 28, 2014

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Abstract:

This is the third and final article in a series which prove the fact that a K-stable Fano manifold admits a Kähler-Einstein metric. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle approaches 2$\pi$. We also put all our technical results together to complete the proof of the main theorem.

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