On the classification of ALE K\"ahler manifolds
  The underlying complex structure of an ALE K\"ahler manifold is exhibited as a resolution of a deformation of an isolated quotient singularity. As a consequence, there exist only finitely many diffeomorphism types of minimal ALE K\"ahler surfaces with a given group at infinity. 
Hans-Joachim Hein, Rares Rasdeaconu, Ioana Suvaina
math.DG math.AG