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

By I. Şuvaina. 2011

46 citations recorded by the source corpus.

Let $${N_0={\mathbb C}^2/H}$$ be an isolated quotient singularity with $${H\subset U(2)}$$ a finite subgroup. We show that for any $${\mathbb Q}$$ -Gorenstein smoothings of N0 a nearby fiber admits ALE Ricci-flat Kähler metrics in any Kähler class. Moreover, we generalize Kronheimer’s results on hyperkähler 4-manifolds (J Differ Geom 29(3):685–697, 1989), by giving an explicit classification of the ALE Ricci-flat Kähler surfaces. We construct ALF Ricci-flat Kähler metrics on the above non-simply connected manifolds. These provide new examples of ALF Ricci-flat Kähler 4-manifolds, with cubic volume growth and cyclic fundamental group at infinity.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/72bc5c6a1f4d4faa72fcb41a296365366bb66be2

Citations in the corpus

• Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein metrics (2012, unknown): “For sake of completeness, even if we will not use it in our proof, we should remark that it is known that local smoothings of T -singularities admit asymptotically conical Calabi-Yau metrics [35] [59].”