= Negative curves of a big real divisor lie in finitely many divisors
Write a big real <Cartier divisor> on an integral <projective variety> as $D\sim_{\mathbb R}B+E$, with $B$ <ample> and $E$ effective real Cartier. Every curve outside $\operatorname{Supp}E$ has $D\cdot C=B\cdot C+E\cdot C>0$. Therefore curves negative against $D$ lie in finitely many support components of codimension one. On a <projective scheme> use <componentwise bigness on a projective scheme> and collect the supports on its finitely many integral components; codimension one is taken in the relevant component.
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