Bulletin of the Korean Mathematical Society ( Vol.43 NO.4 / 2006 ) Title On the projective fourfolds with almost numerically positive canonical divisors(ENG) Author Shigetaka Fukuda MSC 14E30, 14J35 Publication Page 763-770 Page Abstract 1. Introduction 2. The proof of Main Theorem 3. The proof of Theorem Own Status Keyword almost numerically positive, of general type, Kodaira dimension Note Summary 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. Attach [DVI]  [PDF]