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

• Ivan A. Cheltsov ^[1] ; Yanir A. Rubinstein ^[3] ; Kewei Zhang ^[2]
  1. [1] University of Edinburgh

     University of Edinburgh

     Reino Unido

     
  2. [2] Higher School of Economics, National Research University

     Higher School of Economics, National Research University

     Rusia

     
  3. [3] University of Maryland, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 2, 2019
• Idioma: inglés
• DOI: 10.1007/s00029-019-0473-z
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• Resumen

  • 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.