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

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Abstract

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.

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Authors and Affiliations

  1. University of Edinburgh, Edinburgh, UK

    Ivan A. Cheltsov

  2. Peking University, Beijing, China

    Kewei Zhang

  3. University of Maryland, College Park, USA

    Yanir A. Rubinstein & Kewei Zhang

  4. HSE University, Moscow, Russia

    Ivan A. Cheltsov

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  1. Ivan A. Cheltsov
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  2. Yanir A. Rubinstein
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  3. Kewei Zhang
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Correspondence to Yanir A. Rubinstein.

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Research supported by NSF Grant DMS-1515703 and the China Scholarship Council award 201706010020. We thank C. Li for comments on an earlier version, and a referee for a very careful reading.

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Cheltsov, I.A., Rubinstein, Y.A. & Zhang, K. Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces. Sel. Math. New Ser. 25, 34 (2019). https://doi.org/10.1007/s00029-019-0473-z

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