Birkar's Stein-degree conjecture for log Calabi-Yau pairs: the contraction-to-a-point case for ordinary pairs

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Revised edition (October 6, 2026): Conditional good minimal models for compact Kähler fourfolds evidence for this event

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VibeMathed record: Birkar's Stein-degree conjecture for log Calabi-Yau pairs: the contraction-to-a-point case for ordinary pairs evidence for this event

Theorem 1.1: for every field $k$ of characteristic zero and every normal integral projective lc $\mathbb Q$-pair $(X,B)$ of dimension $d$ with $H^0(X,\mathcal O_X)=k$, $B\ge0$ and $K_X+B\sim_{\mathbb Q}0$, every prime component $S$ of $B$ with coefficient at least $t$ satisfies $[k_S:k]\le N(d,t)$, where $k_S$ is the algebraic closure of $k$ in $k(S)$; this bounds the Stein degree of $S$. It covers only the contraction to $\mathrm{Spec}\,k$ and ordinary pairs; the general fibration form of the conjecture and generalized pairs are not treated. parent of this event

Birkar's Stein-degree conjecture for log Calabi-Yau pairs: the contraction-to-a-point case for ordinary pairs evidence for this event

The 5 October appendix calling projective log abundance conditional evidence for this event

Birkar's Stein-degree conjecture for log Calabi-Yau pairs: the contraction-to-a-point case for ordinary pairs parent of this event

Birkar, Stein degree of proper morphisms (arXiv 2603.23939), Conjecture 11.1 evidence for this event