{"id":"openai-math/B-semiampleness-for-compact-log-smooth-Kahler-fibrations","pdf":"https://github.com/openai/math/blob/main/preprints/B-semiampleness-for-compact-log-smooth-Kahler-fibrations-September-10-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/B-semiampleness-for-compact-log-smooth-Kahler-fibrations-September-10-2026","tags":["kahler-geometry","complex-geometry","semiampleness"],"score":0,"title":"B-semiampleness for compact log-smooth Kähler fibrations","domain":"Algebraic and complex geometry","family":"033","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove the compact log-smooth Kähler case of b-semiampleness. Let $`f:Y\\to X`$ be a surjective holomorphic map with connected fibers between smooth compact connected Kähler manifolds, and let Δ be an effective rational divisor with simple normal crossing support and coefficients in $`[0,1]`$, with $`K_Y+\\Delta\\sim_{\\mathbb Q}f^*L`$ for $`L\\in\\mathop{\\mathrm{Pic}}\\nolimits (X)_{\\mathbb Q}`$. There is a smooth compact Kähler modification $`S\\to X`$ for which the threshold-moduli line satisfies $`M_{S_1}=\\nu^*M_S`$ in $`\\mathop{\\mathrm{Pic}}\\nolimits (S_1)_{\\mathbb Q}`$ for every smooth…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-10","reactions":{},"formalized":false,"family_title":"Iitaka subadditivity, variation, and logarithmic additivity"}