On the projective fourfolds with almost numerically positive canonical divisors

Details On the projective fourfolds with almost numerically positive canonical divisors On the projective fourfolds with almost numerically positive canonical divisors

2004-09-06

arxiv.org/abs/math/0409078v7

Bull. Korean Math. Soc. 43(2006), no. 4, 763--770

Mathematics

Algebraic Geometry

9 pages, LaTeX2e; with minor changes

Scientific paper

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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