ALE Ricci-flat Kahler metrics and deformations of quotient surface singularities
Abstract
Let N0 = C2/H be an isolated quotient singularity with H in U (2) a finite subgroup. We show that for any Q-Gorenstein smoothings of N0 a nearby fiber admits ALE Ricci-flat Kahler metrics in any Kahler class. Moreover, we generalize Kronheimer's results on hyperkahler 4-manifolds, by giving an explicit classification of the ALE Ricci-flat Kahler surfaces. We construct ALF Ricci-flat Kahler metrics on the above non-simply connected manifolds. These provide new examples of ALF Ricci-flat Kahler 4-manifolds, with cubic volume growth and cyclic fundamental group at infinity.
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