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Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

   
 

 

Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than $ 2\pi$


Authors: Xiuxiong Chen, Simon Donaldson and Song Sun
Journal: J. Amer. Math. Soc. 28 (2015), 199-234
MSC (2010): Primary 53C55
Published electronically: March 28, 2014
MathSciNet review: 3264767
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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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Xiuxiong Chen
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651 – and – School of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, PR China
Email: xiu@math.sunysb.edu

Simon Donaldson
Affiliation: Department of Mathematics, Imperial College London, London, U.K.
Email: s.donaldson@imperial.ac.uk

Song Sun
Affiliation: Department of Mathematics, Imperial College London, London, U.K.
Email: s.sun@imperial.ac.uk

DOI: https://doi.org/10.1090/S0894-0347-2014-00800-6
Received by editor(s): March 8, 2013
Received by editor(s) in revised form: October 4, 2013, and January 13, 2014
Published electronically: March 28, 2014
Additional Notes: The first author was partly supported by National Science Foundation grant No 1211652; the last two authors were partly supported by the European Research Council award No 247331.
Article copyright: © Copyright 2014 American Mathematica Society