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On log canonical divisors that are log quasi-numerically positive

Shigetaka Fukuda
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Abstract

Let $(X, Δ)$ be a four-dimensional log variety that is projective over the field of complex numbers. Assume that $(X, Δ)$ is not Kawamata log terminal (klt) but divisorial log terminal (dlt). 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 $K_X + Δ$ is log quasi-numerically positive on $(X, Δ)$ then it is semi-ample.

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Shigetaka Fukuda. 2004-09-25. On log canonical divisors that are log quasi-numerically positive. https://arxiv.org/abs/math/0309337

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