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Concerning my previous question Non simply connected HyperKähler 4-manifolds without ALE metrics the following question occurred to me:

Is there any open Ricci-flat ALE 4-manifold other than Hyper-Kahler ALE 4-manifolds?

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1 Answer 1

see Ioana Suvaina, ALE Ricci-flat metrics and deformations of quotient surface singularities, remark 4.5

http://arxiv.org/abs/1102.2672

(this reference was also in one of the answers to your previous question)

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