Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 033-03. The reverse logarithmic Kodaira inequality and additivity
Manuscript map · lines 3095–3104
OpenAI@2026-10-07#rem:oai-p-033-03
Authors: OpenAI. Family 033.
Title: The reverse logarithmic Kodaira inequality and additivity.
Abstract: We prove the reverse logarithmic Kodaira inequality for a surjective connected-fiber morphism $f:(X,E){}to(Y,D)$ of smooth projective reduced simple-normal-crossing pairs, with ${}mathop{{}mathrm{Supp}}{}nolimits (f{}*D){}subseteq{}mathop{{}mathrm{Supp}}{}nolimits E$, such that X and every boundary stratum are smooth over $Y{}setminus{}mathop{{}mathrm{Supp}}{}nolimits D$. 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.
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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