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Exceptional del Pezzo Hypersurfaces

Journal of Geometric Analysis volume 20, pages 787–816 (2010)Cite this article

Abstract

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).

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Authors and Affiliations

  1. School of Mathematics, The University of Edinburgh, Edinburgh, EH93JZ, UK

    Ivan Cheltsov

  2. Department of Mathematics, POSTECH, Pohang, Kyungbuk, 790-784, Korea

    Jihun Park

  3. School of Mathematics, The University of Edinburgh, Edinburgh, EH9 3JZ, UK

    Constantin Shramov

Authors
  1. Ivan Cheltsov
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  2. Jihun Park
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  3. Constantin Shramov
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Corresponding author

Correspondence to Ivan Cheltsov.

Additional information

Communicated by Steven Krantz.

All varieties are assumed to be complex, projective, and normal unless otherwise stated.

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Cheltsov, I., Park, J. & Shramov, C. Exceptional del Pezzo Hypersurfaces. J Geom Anal 20, 787–816 (2010). https://doi.org/10.1007/s12220-010-9135-2

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  • DOI: https://doi.org/10.1007/s12220-010-9135-2

Keywords

  • 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