Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2𝜋

Chen, Xiuxiong; Donaldson, Simon; Sun, Song

doi:10.1090/S0894-0347-2014-00800-6

Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath$2\pi$
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by Xiuxiong Chen, Simon Donaldson and Song Sun

J. Amer. Math. Soc. 28 (2015), 199-234

DOI: https://doi.org/10.1090/S0894-0347-2014-00800-6

Published electronically: March 28, 2014

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Abstract:

This is the second of a series of three papers 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 is less than 2${\pi }$. We show that these are in a natrual way projective algebraic varieties. In the case when the limiting variety and the limiting divisor are smooth we show that the limiting metric also has standard cone singularities.

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