OpenAI · 033-02 · 2026-09-26 · Algebraic and complex geometry
Logarithmic Kodaira dimension and whole-fiber variation
preprints/Logarithmic-Kodaira-dimension-and-whole-fiber-variation-September-26-2026
Family 033. Campana's orbifold Iitaka conjecture and logarithmic subadditivity.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves Campana's orbifold Iitaka subadditivity conjecture for smooth Fujiki-class- manifolds with rational simple-normal-crossing boundaries. For projective fibrations of smooth complex quasi-projective varieties with connected fibers, general fiber , and , proves Popa's inequality , where variation measures the whole geometric generic fiber.
We prove the logarithmic Iitaka–Viehweg inequality for projective surjective morphisms with connected fibers between smooth complex quasi-projective varieties whose base has nonnegative logarithmic Kodaira dimension. The variation measures the birational field of definition of the whole geometric generic fiber. This resolves Popa's logarithmic variation conjecture positively.
Preprint source and Lean scope
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A Lean scope note is stored for family 033, but it does not name this preprint. It names 033-03. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.