I am trying to understand $\mathbb Q$-Gorenstein smoothings, and especially the third condition in the following definition. >**Definition.** For a normal projective surface $X$ with quotient singularities, a $\mathbb Q$-Gorenstein smoothing is a one-parameter flat family of projective surfaces $\Psi \colon \mathcal X \rightarrow \Delta$ over a small disk $\Delta$, which satisfies the following three conditions: >1. the general fibre $X_t$ is a smooth projective surface, >2. the central fibre $X_0$ is $X$, >3. the canonical divisor $K_{\mathcal X / \Delta}$ is $\mathbb Q$-Cartier. We say that $X'$ is a $\mathbb Q$-Gorenstein smoothing of $X$ if there exists such a family $\Psi \colon \mathcal X \to \Delta $ as above such that $X'=\Psi^{-1}(t)$ for some $t\in \Delta$. For example, I am trying to understand the following. >**Question 1.** Assume that there exists a fixed integer $m$ such $mK_{X_t}$ is Cartier for every $t$. Is there any example where 3rd condition is not satisfied? >**Question 2.** If the total space of the family is $\mathbb Q$-Gorenstein, is it true that the 3rd condition is satisfied? References with examples would be appreciated.