{"id":"openai-math/Minimal-models-in-numerical-dimension-one","pdf":"https://github.com/openai/math/blob/main/preprints/Minimal-models-in-numerical-dimension-one-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Minimal-models-in-numerical-dimension-one-September-24-2026","tags":["birational-geometry","minimal-models","algebraic-varieties"],"score":0,"title":"Minimal models in numerical dimension one","domain":"Algebraic and complex geometry","family":"036","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We resolve the numerical-dimension-one case of the minimal-model conjecture for smooth connected complex projective varieties of dimension at least three. If K X is pseudo-effective and $`\\kappa_\\sigma(X,K_X)=1`$, with κ σ defined by section growth with a fixed ample twist, then X admits a projective ℚ-factorial terminal minimal model.","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"}