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ON THE PROJECTIVE FOURFOLDS WITH ALMOST NUMERICALLY POSITIVE CANONICAL DIVISORS
Fukuda, Shigetaka Korean Mathematical Society 2006 대한수학회보 Vol.43 No.4
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 ';he viewpoint of geometric Kodaira dimension. We note that the converse does not hold for simple abelian varieties.
On the projective fourfolds with almost numerically positive canonical divisors
Shigetaka Fukuda 대한수학회 2006 대한수학회보 Vol.43 No.4
LetX be a four-dimensional projective variety denedover the eld of complex numbers with only terminal singularities.We prove that if the intersection number of the canonical divisorKwith every very general curve is positive (K is almost numericallypositive) then every very general proper subvariety ofX is of generaltype in the viewpoint of geometric Kodaira dimension. We notethat the converse does not hold for simple abelian varieties.
Algebraic Fiber Space Whose Generic Fiber and Base Space Are of Almost General Type
Fukuda, Shigetaka Department of Mathematics 2014 Kyungpook mathematical journal Vol.54 No.2
We assume that the existence and termination conjecture for flips holds. A complex projective manifold is said to be of almost general type if the intersection number of the canonical divisor with every very general curve is strictly positive. Let f be an algebraic fiber space from X to Y. Then the manifold X is of almost general type if every very general fiber F and the base space Y of f are of almost general type.