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On the projective fourfolds with almost numerically positive canonical divisors

Shigetaka Fukuda
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Abstract

Let $X$ be a four-dimensional projective variety defined over the field of complex numbers with only terminal singularities. We prove that if the intersection number of the canonical divisor $K$ with every very general curve is positive ($K$ is almost numerically positive) then every very general proper subvariety of $X$ is of general type in the viewpoint of geometric Kodaira dimension. We note that the converse does not hold for simple abelian varieties.

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Shigetaka Fukuda. 2005-02-01. On the projective fourfolds with almost numerically positive canonical divisors. https://arxiv.org/abs/math/0409078

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