{"id":"openai-math/Logarithmic-Kodaira-dimension-and-whole-fiber-variation","pdf":"https://github.com/openai/math/blob/main/preprints/Logarithmic-Kodaira-dimension-and-whole-fiber-variation-September-26-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Logarithmic-Kodaira-dimension-and-whole-fiber-variation-September-26-2026","tags":["algebraic-geometry","kodaira-dimension","fiber-variation","iitaka-fibration"],"score":0,"title":"Logarithmic Kodaira dimension and whole-fiber variation","domain":"Algebraic and complex geometry","family":"033","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"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.","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"}