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arXiv · 2509.20948

Stein degree on log Calabi-Yau fibrations

Caucher Birkar·Santai Qu
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Abstract

We prove a conjecture proposed by the first author on boundedness of Stein degree of divisors on log Calabi-Yau fibrations. More precisely, for $d\in \mathbb{N}$ and $t\in (0,1]$, let $(X, B)\to Z$ be a log Calabi-Yau fibration of relative dimension $d$, and let $S$ be a horizontal$/Z$ irreducible component of $B$ whose coefficient in $B$ is $\ge t$. We show that the number of irreducible components of a general fibre of $S\to Z$ is bounded from above depending only on $d,t$.

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Caucher Birkar, Santai Qu. 2025-09-25. Stein degree on log Calabi-Yau fibrations. https://arxiv.org/abs/2509.20948

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