Journal of Geometric Analysis

, Volume 20, Issue 4, pp 787–816 | Cite as

Exceptional del Pezzo Hypersurfaces

  • Ivan Cheltsov
  • Jihun Park
  • Constantin Shramov


We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in ℙ(a 0,a 1,a 2,a 3). As a corollary we obtain the existence of orbifold Kähler-Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well-formed del Pezzo weighted hypersurfaces in ℙ(a 0,a 1,a 2,a 3).


Global log canonical threshold Alpha-invariant of Tian Del Pezzo orbifold Weighted hypersurface Kähler–Einstein metric Exceptional Fano variety Weakly exceptional Fano variety Exceptional singularity Weakly exceptional singularity 

Mathematics Subject Classification (2000)

14J45 32Q20 14J70 14Q10 32S25 


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© Mathematica Josephina, Inc. 2010

Authors and Affiliations

  1. 1.School of MathematicsThe University of EdinburghEdinburghUK
  2. 2.Department of MathematicsPOSTECHPohangKorea
  3. 3.School of MathematicsThe University of EdinburghEdinburghUK

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