On log canonical divisors that are log quasi-numerically positive

2003/09/30 by Shigetaka Fukuda
Mathematics · #math.AG #msc:14E30

paper · pdf

published as Cent. Eur. J. Math. 2 (2004), no. 3, 377--381(electronic) · 4 pages, LaTeX2e, the published version

arxiv created 2004/09/25 · arxiv updated 2009/12/01

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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