I'm seaching for a proof of the theorem below. Do you know any reference?
Consider $f:X\rightarrow Y$ projective birational map between normal varieties and $\mathbb{R}$ cartier divisor $D$ whose support is contained in the exceptional set of $f$ .
If the exceptional set is connected and $D$ is non zero $f$-nef,
Then the support of $D$ is equal to the exceptional set of $f$ and all of coefficient of $D$ is negative.
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- 1$\begingroup$ This is Lemma 3.39 of Koll\'ar--Mori. There the result is stated for $\mathbb Q$-divisors but the proof seems to work just as well for $\mathbb R$-divisors. $\endgroup$Lazzaro Campeotti– Lazzaro Campeotti2024-04-22 08:10:17 +00:00Commented Apr 22, 2024 at 8:10
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