On log canonical divisors that are log quasi-numerically positive

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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.
4 pages, LaTeX2e, the published version

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Algebraic Geometry, 14E30

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http://salesiana.dossiersoluciones.com/handle/123456789/68628

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0309337
 http://arxiv.org/abs/math/0309337
 Cent. Eur. J. Math. 2 (2004), no. 3, 377--381(electronic)

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arXiv