{"id":"openai-math/Numerical-Semiampleness-of-Nef-Adjoint-Divisors","pdf":"https://github.com/openai/math/blob/main/preprints/Numerical-Semiampleness-of-Nef-Adjoint-Divisors-October-3-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Numerical-Semiampleness-of-Nef-Adjoint-Divisors-October-3-2026","tags":["algebraic-geometry","minimal-model-program","birational-geometry"],"score":0,"title":"Numerical Semiampleness of Nef Adjoint Divisors","domain":"Algebraic and complex geometry","family":"036","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove the Generalised Abundance Conjecture: if $`(X,B)`$ is a projective klt ℚ-pair over an algebraically closed field of characteristic zero, $`K_X+B`$ is pseudo-effective, M is a nef ℚ-Cartier divisor on X , and $`K_X+B+M`$ is nef, then $`K_X+B+M`$ is numerically equivalent to a semiample ℚ-Cartier divisor on X .","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-03","reactions":{},"formalized":false,"family_title":"Numerical semiampleness and generalized minimal models"}