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

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 Kahler-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.

arXiv commentv2: minor changes

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Cited by in corpus (16)

• Optimal destabilization of K-unstable Fano varieties via stability thresholds
• Openness of uniform K-stability in families of $\mathbb{Q}$-Fano varieties
• K-stability of Fano varieties: an algebro-geometric approach
• A quantization proof of the uniform Yau-Tian-Donaldson conjecture
• Basis divisors and balanced metrics
• Delta-invariants for Fano varieties with large automorphism groups
• Continuity of delta invariants and twisted Kähler--Einstein metrics
• Geometric flow, Multiplier ideal sheaves and Optimal destabilizer for a Fano manifold
• On the uniform K-stability for some asymptotically log del Pezzo surfaces
• K-stability of Gorenstein Fano group compactifications with rank two
• Valuative invariants with higher moments
• Emergent complex geometry
• Simply connected Sasaki-Einstein rational homology 5-spheres
• On the body of ample angles of asymptotically log Fano varieties
• Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one
• Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII