M. Reid has a theorem as following:
Let $X$ be a non-singular projective complex surface, $L \subset \Omega^1_X$ be a line bundle. If $h^0(L^{\otimes n})\geq2$ for some $n\geq 1$, then there is a moephism $f:X\rightarrow C$ of $X$ onto a nonsingular curve $C$ of positive genus, and a ramification divisor $D$ (of the map $f$) such that $L$ and $f^*(\Omega^1_C)(D)$ coincide as sheaves.
How to derive the following statements?
(a) there exists a constant $k$ such that for all $n$ $$h^0(L^{\otimes n} )< nk$$ (b) $L$ is not in the positive cone of $NS(X)$