Existence and deformations of Kahler-Einstein metrics on smoothable   Q-Fano varieties
  We prove the existence of Kahler-Einstein metrics on Q-Gorenstein smoothable, K-polystable Q-Fano varieties, and we show how these metrics behave, in the Gromov-Hausdorff sense, under Q-Gorenstein smoothings. 
Cristiano Spotti, Song Sun, Chengjian Yao
math.DG math.AG math.CV