= Fixed-part elimination on a K3 surface
If $D$ is a nontrivial <nef divisor> on a <K3 surface> with $D^2=0$, its <complete linear system of a divisor> has no fixed part. Write $D=F+M$. Nefness of $D$ and $M$ gives $D\cdot F=D\cdot M=M^2=M\cdot F=F^2=0$. But a nonzero fixed part satisfies $h^0(F)=1$, while <Riemann–Roch theorem for algebraic surfaces> and <Serre duality> would give $h^0(F)\geq2$ if $F^2=0$. Hence $F=0$. Two movable members with no common component have intersection zero and are disjoint, so the system is <basepoint-free> and has <Iitaka dimension> one.
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