Log Canonical Thresholds of Del Pezzo Surfaces

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Abstract.We study global log canonical thresholds of del Pezzo surfaces.All varieties are assumed to be defined over $${\mathbb{C}}$$.

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Exceptional del Pezzo Hypersurfaces (2008, background): “The global log canonical thresholds of such del Pezzo surfaces have been considered either implicitly or explicitly in [1, 4, 8, 12].”
On the moduli of Kähler-Einstein Fano manifolds (2012, background): “hich is linearly equivalent to half of the anti-canonical divisor (i.e. −KX ∼= 2H) can be a smooth del Pezzo surface for which the Conjecture 1.5 is solved with respect to anticanonical polarization ([Che07]). 3. A conjecture The author expects that K-polystable objects form projective moduli in gen”
Explicit Gromov-Hausdorff compactifications of moduli spaces of K\"ahler-Einstein Fano manifolds (2017, result): “There have been important recent progresses towards this, see for example [28, 26, 27, 51] as well as older results based on α-invariant/log canonical threshold and multiplier ideal sheaves techniques, for example [55, 60, 62, 46, 19, 12, 14], or with large symmetries, e.”
Alpha invariant and K-stability of Q-Fano varieties (2010, background): “On the other hand, it is known that α(X) ≥ 2 3 for n ≥ 6 case and they have Kähler-Einstein metrics (see [34] and [5]).”