OpenAI · 033-03 · 2026-09-26 · Algebraic and complex geometry
The reverse logarithmic Kodaira inequality and additivity
preprints/The-reverse-logarithmic-Kodaira-inequality-and-additivity-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 reverse logarithmic Kodaira inequality for a surjective connected-fiber morphism of smooth projective reduced simple-normal-crossing pairs, with , such that X and every boundary stratum are smooth over . Together with logarithmic subadditivity, the inequality gives additivity, including both negative-infinity cases. This resolves Popa's logarithmic additivity conjecture positively in the projective reduced-SNC, stratum-smooth setting.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 033: Iitaka subadditivity, variation, and logarithmic additivity. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.