= Solution
The relevant invariant of a divisor is its <Iitaka dimension>, also called its Kodaira dimension. If two linearly independent <global sections> $s,t$ occur in $H^0(X,nH)$, their ratio is a nonconstant <rational function>. The sections $s^q,s^{q-1}t,\ldots,t^q$ are linearly independent, because a nonconstant rational function over an algebraically closed field is transcendental over that field. Thus some <complete linear system of a divisor> has positive-dimensional image, contradicting $\kappa(H)=0$.
Consequently $h^0(X,nH)=1$ for every $n>0$; the nonemptiness of $|H|$ supplies a nonzero section in every multiple. Its unique divisor is entirely fixed. Hence \b[every movable part $M_n$ is zero].
Back to article page
