Mathematics – Algebraic Geometry
Scientific paper
2003-09-20
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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