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On the non-vanishing conjecture and existence of log minimal models. (English) Zbl 1390.14052

The non-vanishing conjecture states that if \((X,B)\) is projective log canonical pair such that \(K_X+B\) is pseudo-effective, then there exists an effective \(\mathbb R\)-divisor \(D\) such that \(K_X+B\sim _{\mathbb R}D\). In this paper, the author shows that in order to prove this conjecture, it suffices to prove the analogous statement when \(X\) is a smooth projective variety and \(B=0\).

MSC:

14E30 Minimal model program (Mori theory, extremal rays)