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ON THE PROJECTIVE FOURFOLDS WITH ALMOST NUMERICALLY POSITIVE CANONICAL DIVISORS

  • Published : 2006.11.30

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 ';he viewpoint of geometric Kodaira dimension. We note that the converse does not hold for simple abelian varieties.

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Cited by

  1. Algebraic Fiber Space Whose Generic Fiber and Base Space Are of Almost General Type vol.54, pp.2, 2014, https://doi.org/10.5666/KMJ.2014.54.2.203