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 On the projective fourfolds with almost numerically positive canonical divisors Bull. Korean Math. Soc. 2006 Vol. 43, No. 4, 763-770 Printed December 1, 2006 Shigetaka Fukuda Gifu Shotoku Gakuen University 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. Keywords : almost numerically positive, of general type, Kodaira dimension MSC numbers : 14E30, 14J35 Downloads: Full-text PDF