{"id":"openai-math/Bounded-klt-complements-for-Fano-contractions","pdf":"https://github.com/openai/math/blob/main/preprints/Bounded-klt-complements-for-Fano-contractions-September-25-2026/Bounded-klt-complements-for-Fano-contractions-September-25-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Bounded-klt-complements-for-Fano-contractions-September-25-2026","tags":["birational-geometry","fano-varieties","klt-complements"],"score":0,"title":"Bounded klt complements for Fano contractions","domain":"Algebraic and complex geometry","family":"066","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"For fixed dimension d and positive rational ϵ , we prove that every ϵ -log-canonical Fano contraction over an algebraically closed field of characteristic zero admits, near each closed base point, a klt complement of index bounded only by d and ϵ . Over ℂ, we also obtain monotone klt complements for Fano type pairs with nef anti-log-canonical divisor and coefficients in a fixed finite rational set. This proves the finite-rational-coefficient form of Shokurov's bounded-klt-complement conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Bounded klt complements for Fano contractions"}