TITLE: Kähler small resolution of 3-dim ADE singularities
QUESTION [5 upvotes]: In Tristan Hübschs book on Calabi-Yau manifolds it is stated that 3-dimensional ADE singularities admit a crepant resolution but this resolution does not need to be Kähler.
Are there some results on when one of these singularities admit a small resolution that is Kähler?
Best,
Peter

REPLY [2 votes]: An analysis of when this type of singularities admits (Kähler) small resolutions is carried out in this paper by Sheldon Katz, see also this question and the answer to
this one.