{"id":"openai-math/Minimal-models-and-Mori-fibre-spaces-for-generalized-log-canonical-Q-pairs","pdf":"https://github.com/openai/math/blob/main/preprints/Minimal-models-and-Mori-fibre-spaces-for-generalized-log-canonical-Q-pairs-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Minimal-models-and-Mori-fibre-spaces-for-generalized-log-canonical-Q-pairs-September-24-2026","tags":["birational-geometry","minimal-models","log-canonical"],"score":0,"title":"Minimal models and Mori fibre spaces for generalized log canonical Q-pairs","domain":"Algebraic and complex geometry","family":"036","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We resolve the existence form of the minimal-model conjecture for projective generalized log canonical ℚ-pairs over algebraically closed fields of characteristic zero. Such a pair admits a minimal model when its adjoint divisor is pseudo-effective, and a Mori fibre space otherwise, while keeping the nef ℚ-Cartier b-divisor fixed. Taking the nef part to be zero gives the corresponding result for ordinary log canonical ℚ-pairs.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Numerical semiampleness and generalized minimal models"}