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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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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