Say $V$ has only canonical singularities iff $V$ is $\mathbb{Q}$-Gorenstein, of finite index $N$ and one of the following equivalent conditions is fulfilled:

1. (1)

   Let $\pi:X\to V$ be a resolution. Let $\alpha$ be a local generator of $\omega_{V}^{[N]}$. The meromorphic pluricanonical form $\pi^{*}\alpha$ is holomorphic.

2. (2)

   Let $\pi:X\to V$ be a resolution. For every $m\in\mathbb{N},\ \pi_{*}\omega_{X}^{[Nm]}=\omega_{V}^{[Nm]}$.

3. (3)

   (Assuming $V$ is an algebraic variety) Let $\pi:X\to V$ be a resolution. Then $K_{X}\cong\pi^{*}K_{V}+\displaystyle\sum a_{E}E$ with $a_{E}\geq 0$ where $\cong$ means numerical equivalence of $\mathbb{Q}$-Cartier divisors and the sum runs over the exceptional divisors of $\pi$.