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Sequence of MMP with scaling cannot be isomorphism

Let $(X,B)$ be a projective klt pair, H is an $\mathbb{R}$-divisor s.t. $K_X+B+H$ is nef. Suppose that we can run $(K_X+B)$-MMP with scaling $H$(that is, the flip exists) and denote $\alpha_i:X \...
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