Consider $X$ be a Calabi-Yau n-fold with at most one ordinary double point singularity. Suppose $X$ is smoothable. Then it is known that the Kuranishi family of $X$ is a smoothing of $X$.
Now, assume $X$ be a Calabi-Yau n-fold with log terminal singularities, then still the Kuranishi family of $X$ can be a smoothing of $X$?
