{"id":"openai-math/Lifting-sections-from-the-reduced-support-of-an-adjoint","pdf":"https://github.com/openai/math/blob/main/preprints/Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Lifting-sections-from-the-reduced-support-of-an-adjoint-September-27-2026","tags":["birational-geometry","log-abundance","minimal-model-program"],"score":0,"title":"Lifting sections from the reduced support of an adjoint","domain":"Algebraic and complex geometry","family":"034","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"For a projective ℚ-factorial dlt pair with effective rational boundary over an algebraically closed field of characteristic zero, we prove that the adjoint has positive Iitaka dimension whenever a nonzero effective Cartier multiple is supported on the coefficient-one boundary and restricts to a semiample line bundle on its whole reduced support. This gives log abundance after nonvanishing in dimension at most four over ℂ.","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"}