{"id":"openai-math/The-reverse-logarithmic-Kodaira-inequality-and-additivity","pdf":"https://github.com/openai/math/blob/main/preprints/The-reverse-logarithmic-Kodaira-inequality-and-additivity-September-26-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-reverse-logarithmic-Kodaira-inequality-and-additivity-September-26-2026","tags":["algebraic-geometry","birational-geometry","kodaira-inequality"],"score":0,"title":"The reverse logarithmic Kodaira inequality and additivity","domain":"Algebraic and complex geometry","family":"033","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":false,"family_title":"Iitaka subadditivity, variation, and logarithmic additivity"}