Abstract
We show that the explicit ALE Ricci-flat Kahler metrics constructed by Eguchi–Hanson, Gibbons–Hawking, Hitchin and Kronheimer, and their free quotients are metrics obtained by Tian–Yau techniques. The proof relies on a construction of good compactifications of \(\mathbb {Q}\)-Gorenstein deformations of quotient surface singularities as log del Pezzo surfaces with only cyclic quotient singularities at infinity.
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