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The purpose of this article is to develop techniques for estimating basis logcanonical thresholds on logarithmic surfaces. To that end, we develop new localintersection estimates that imply log canonicity. Our main motivation andapplication is to show the existence of Kahler-Einstein edge metrics on all butfinitely many families of asymptotically log del Pezzo surfaces, partiallyconfirming a conjecture of two of us. In an appendix we show that the basis logcanonical threshold of Fujita-Odaka coincides with the greatest lower Riccibound invariant of Tian.

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