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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.
##### MSC:
 1.4e+31 Minimal model program (Mori theory, extremal rays)
##### Keywords:
divisorial log terminal; numerically positive; semi-ample
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##### References:
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