ALE Ricci-flat Kahler metrics and deformations of quotient surface singularities

Details ALE Ricci-flat Kahler metrics and deformations of quotient surface singularities ALE Ricci-flat Kahler metrics and deformations of quotient surface singularities

2011-02-14

arxiv.org/abs/1102.2672v1

Mathematics

Differential Geometry

Scientific paper

Let N_0 = C^2/H be an isolated quotient singularity with H in U (2) a finite subgroup. We show that for any Q-Gorenstein smoothings of N_0 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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