{"id":"openai-math/Log-abundance-in-characteristic-zero","pdf":"https://github.com/openai/math/blob/main/preprints/Log-abundance-in-characteristic-zero-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Log-abundance-in-characteristic-zero-September-24-2026","tags":["algebraic-geometry","log-abundance","birational-geometry","minimal-model-program"],"score":0,"title":"Log abundance in characteristic zero","domain":"Algebraic and complex geometry","family":"034","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove the rational-boundary log abundance conjecture in every dimension over algebraically closed fields of characteristic zero: every nef ℚ-Cartier log canonical divisor on a projective log canonical pair with effective rational boundary is semiample. Over ℂ, the proof also establishes canonical nonvanishing for smooth projective varieties in every dimension.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity"}