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