On log canonical divisors that are log quasi-numerically positive

Details On log canonical divisors that are log quasi-numerically positive On log canonical divisors that are log quasi-numerically positive

2003-09-20

arxiv.org/abs/math/0309337v5

Cent. Eur. J. Math. 2 (2004), no. 3, 377--381(electronic)

Mathematics

Algebraic Geometry

4 pages, LaTeX2e, the published version

Scientific paper

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 (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 $K_X + \Delta$ is log quasi-numerically positive on $(X, \Delta)$ then it is semi-ample.

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