Log canonical thresholds of certain Fano hypersurfaces

Ivan Cheltsov, Jihun Park, Joonyeong Won

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16 Scopus citations


We study log canonical thresholds on quartic threefolds, quintic fourfolds, and double spaces. As an important application, we show that they have Kähler-Einstein metrics if they are general.

Original languageEnglish
Pages (from-to)51-79
Number of pages29
JournalMathematische Zeitschrift
Issue number1-2
StatePublished - Feb 2014

Bibliographical note

Funding Information:
The authors would like to express their sincere appreciation to the referee for the invaluable comments. The referee’s comments enable the authors to improve their results as well as their exposition. In particular, the referee pointed out a gap in the previous proof of Lemma 2.17. To fix the gap, the authors introduce new generality conditions to quintic fourfolds. This serious revision was done while the first two authors stay at Hausdorff Research Institute for Mathematics at Bonn, Germany for Research in Groups Program from 1st of August to 4th of September 2012. Ivan Cheltsov and Jihun Park would like to thank the institute for their support. Jihun Park has been supported by the Research Center Program (Grant No. CA1205-02) of Institute for Basic Science and SRC-GAIA(Grant No. 2011-0030795) of the National Research Foundation in Korea.


  • Anticanonical linear system
  • Fano variety
  • Kähler-Einstein metric
  • Log canonical threshold


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