Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 034-08. Schnell fiber spaces and good canonical models
Manuscript map · lines 3195–3204
OpenAI@2026-10-07#rem:oai-p-034-08
Authors: OpenAI. Family 034.
Title: Schnell fiber spaces and good canonical models.
Abstract: 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 m0. 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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