{"id":"openai-math/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs","pdf":"https://github.com/openai/math/blob/main/preprints/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Arithmetic-Stein-degree-bounds-for-log-Calabi-Yau-pairs-September-25-2026","tags":["algebraic-geometry","log-calabi-yau","birational-geometry"],"score":0,"title":"Arithmetic Stein-degree bounds for log Calabi–Yau pairs","domain":"Algebraic and complex geometry","family":"034","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"Fix d ≥ 1 and t > 0. Let $`(X,B)`$ be an ordinary projective log canonical ℚ-pair of dimension d over a characteristic-zero field k , with X normal and integral, $`H^0(X,\\mathcal O_X)=k`$, B effective, and $`K_X+B\\sim_{\\mathbb Q}0`$. We prove that every prime component S of B with coefficient at least t satisfies $`[k_S:k]\\leq N(d,t)`$, where k S is the relative algebraic closure of k in $`k(S)`$. This also bounds the Stein degree of S over k , proving the contraction-to-a-point formulation of Birkar's Stein-degree conjecture for ordinary ℚ-pairs.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity"}