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

## 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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## Additional Information

**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
- MR Author ID: 632654
- 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.
- MR Author ID: 879901
- Email: s.sun@imperial.ac.uk
- 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.
- © Copyright 2014 American Mathematica Society
- Journal: J. Amer. Math. Soc.
**28**(2015), 199-234 - MSC (2010): Primary 53C55
- DOI: https://doi.org/10.1090/S0894-0347-2014-00800-6
- MathSciNet review: 3264767