Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 034-12. Arithmetic Stein-degree bounds for log Calabi–Yau pairs
Manuscript map · lines 3235–3244
OpenAI@2026-10-07#rem:oai-p-034-12
Authors: OpenAI. Family 034.
Title: Arithmetic Stein-degree bounds for log Calabi–Yau pairs.
Abstract: 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 kS 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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