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Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces

  • Ivan A. Cheltsov
  • Yanir A. RubinsteinEmail author
  • Kewei Zhang


The purpose of this article is to develop techniques for estimating basis log canonical thresholds on logarithmic surfaces. To that end, we develop new local intersection estimates that imply log canonicity. Our main motivation and application is to show the existence of Kähler–Einstein edge metrics on all but finitely many families of asymptotically log del Pezzo surfaces, partially confirming a conjecture of two of us. In an appendix we show that the basis log canonical threshold of Fujita–Odaka coincides with the greatest lower Ricci bound invariant of Tian.

Mathematics Subject Classification

Primary 32Q20 Secondary 14J45 14C20 32Q15 32Q26 32Q30 



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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ivan A. Cheltsov
    • 1
    • 4
  • Yanir A. Rubinstein
    • 3
    Email author
  • Kewei Zhang
    • 2
    • 3
  1. 1.University of EdinburghEdinburghUK
  2. 2.Peking UniversityBeijingChina
  3. 3.University of MarylandCollege ParkUSA
  4. 4.HSE UniversityMoscowRussia

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