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On log canonical divisors that are log quasi-numerically positive. (English) Zbl 1071.14019
Summary: Let \((X, \Delta)\) be a four-dimensional log variety that is projective over the field of complex numbers. Assume that \((X, \Delta)\) is not Kawamata log terminal but divisorial log terminal. First we introduce the notion of “log quasi-numerically positive”, by relaxing that of “numerically positive”. Next we prove that, if the log canonical divisor \(K_X+\Delta\) is log quasi-numerically positive on \((X,\Delta)\) then it is semi-ample.
14E30 Minimal model program (Mori theory, extremal rays)
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