= Rigidity of a negative curve
{title2=$|C|=\{C\}$}
If an <effective divisor> $D$ is <linearly equivalent> to a <negative curve> $C$, then $D=C$. Otherwise $D\cdot C=C^2<0$ forces $C$ to be a component of $D$, since distinct irreducible curves have nonnegative <intersection multiplicities>. Write $D=C+D'$ with $D'$ effective and linearly equivalent to zero. An <ample divisor> intersects $D'$ positively unless $D'=0$, while linear equivalence forces that intersection to vanish.
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