LOG CANONICAL THRESHOLDS OF SMOOTH FANO THREEFOLDS

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Exceptional del Pezzo Hypersurfaces (2008, background): “The number lct(X) is an algebraic counterpart of the α-invariant of Tian (see [5, 22]).”
Alpha invariant and K-stability of Q-Fano varieties (2010, background): “We note that the definition of lct(X,Σ) in the appendix [7] uses the complex singularity exponent, but it is equivalent to (5).”
A thermodynamical formalism for Monge–Ampère equations, Moser–Trudinger inequalities and Kähler–Einstein metrics (2010, background): “As for the second point above it generalizes a result of Nadel [68] and DemaillyKollar [35] concerning the case when uj is a subsequence of the curve ut appearing in the continuity method (see remark 4.6) and hence the result in the second point above is new even when θ = 0.”