{"id":"openai-math/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds","pdf":"https://github.com/openai/math/blob/main/preprints/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Abundance-after-nonvanishing-for-compact-Kahler-fourfolds-September-27-2026","tags":["birational-geometry","kahler-geometry","minimal-model-program"],"score":0,"title":"Abundance after nonvanishing for compact Kähler fourfolds","domain":"Algebraic and complex geometry","family":"034","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"We prove semiampleness of the actual ℚ-Cartier adjoint $`K_X+\\Delta`$ of a normal connected compact Kähler klt fourfold whenever it is analytically nef and some positive Cartier multiple has a nonzero section. The boundary is effective and rational; the fourfold need not be projective or ℚ-factorial. In Iitaka dimension zero, a positive Cartier multiple is the trivial holomorphic line bundle.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":false,"family_title":"Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity"}