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## Computing α-Invariants of Singular del Pezzo Surfaces

Journal of Geometric Analysis. 2014. Vol. 24. No. October. P. 798-842.
Cheltsov Ivan, Kosta D.

We prove a new local inequality for divisors on surfaces and utilize it to compute α-invariants of singular del Pezzo surfaces, which implies that del Pezzo surfaces of degree one whose singular points are of type A1 , A2 , A3 , A4 , A5 , or A6 are Kähler-Einstein.