Adjunction termination implies uniruledness

Let $X$ be a smooth projective variety of dimension $n$ over $\a0\mathbb{C}$, with canonical divisor $K_X$, and let $L$ be an effective divisor. Say that adjunction terminates in the classical sense for $L$ if there exists an integer $m_0\geq 1$ such that

$$H^0(X,L+mK_X)=0$$

for every integer $m\geq m_0$. Adjunction termination conjecture. If adjunction terminates in the classical sense for $L$, then $X$ is uniruled. The condition implies that $X$ has negative Kodaira dimension, and the conjecture reflects the expectation that varieties of negative Kodaira dimension are uniruled; the statement is presented as an open question.