  We prove the following theorem characterizing Du Bois singularities. Suppose
that $Y$ is smooth and that $X$ is a reduced closed subscheme. Let $\pi : \tld
Y \to Y$ be a log resolution of $X$ in $Y$ that is an isomorphism outside of
$X$. If $E$ is the reduced pre-image of $X$ in $\tld Y$, then $X$ has Du Bois
singularities if and only if the natural map $\O_X \to R \pi_* \O_E$ is a
quasi-isomorphism. We also deduce Koll\'ar's conjecture that log canonical
singularities are Du Bois in the special case of a local complete intersection
and prove other results related to adjunction.
