Let $X$ be a normal projective variety with klt singularities with numerically trivial canonical divisor $K\_X$. 


Does there always exist a Kähler-Einstein metric on $X$?



Kähler-Einstein metrics on singular varieties
Yes, this is a result of Essydieux-Guedj-Zeriahi: "Singular Kähler-Einstein metrics" J. Amer. Math. Soc. 22 (2009), 607-639.


