  Here we investigate the property of effectivity for adjoint divisors. Among
others, we prove the following results:
  (i) A normal projective variety $X$ with at most canonical singularities is
uniruled if and only if for each very ample Cartier divisor $H$ on $X$ we have
$H^0(X, m_0K_X+H)=0$ for some $m_0=m_0(H)>0$.
  (ii) Let $(X,L)$ be a polarized manifold of dimension $4$ and let $t$ be an
integer with $t \ge 3$. If $K_X+tL$ is pseudo-effective, then $H^0(X, K_X+tL)
\ne 0$.
