  We prove that a Cohen-Macaulay normal variety $X$ has Du Bois singularities
if and only if $\pi_*\omega_{X'}(G) \simeq \omega_X$ for a log resolution $\pi:
X' \to X$, where $G$ is the reduced exceptional divisor of $\pi$. Many basic
theorems about Du Bois singularities become transparent using this
characterization (including the fact that Cohen-Macaulay log canonical
singularities are Du Bois).
  We also give a straightforward and self-contained proof that (generalizations
of) semi-log-canonical singularities are Du Bois, in the Cohen-Macaulay case.
It also follows that the Kodaira vanishing theorem holds for semi-log-canonical
varieties and that Cohen-Macaulay semi-log-canonical singularities are
cohomologically insignificant in the sense of Dolgachev.
