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

作者：Suvaina Ioana^*

来源：Annals of Global Analysis and Geometry, 2012, 41(1): 109-123.

DOI：10.1007/s10455-011-9273-1

• ALE Ricci-flat manifolds
• Deformations of quotient singularities

Let N(0) = C(2)/H be an isolated quotient singularity with H subset of 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 (J Differ Geom 29(3):685-697, 1989), 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.

• 出版日期2012-1