ALE Ricci-flat Kahler metrics and deformations of quotient surface singularities
Differential Geometry
2011-02-15 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1102.2672,
title = {ALE Ricci-flat Kahler metrics and deformations of quotient surface singularities},
author = {Ioana Suvaina},
journal= {arXiv preprint arXiv:1102.2672},
year = {2011}
}