Schnell fiber spaces and good canonical models
We prove the Campana–Peternell inequality $\kappa(X)\geq\kappa(D)$ for a smooth connected projective complex variety X and an effective Cartier divisor D whenever $m_0K_X-D$ is pseudo-effective for some positive integer m 0 . For an algebraic fiber space $f\colon X\to Y$ between smooth connected projective complex varieties, the hypothesis that $m_0K_X-f^*H$ is pseudo-effective with H ample Cartier gives $\kappa(X)=\kappa(F)+\dim Y$ for a very general smooth fiber F , as well as nonzero sections of $mK_X-f^*H$ for all sufficiently large divisible m .
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