Stein degree on log Calabi-Yau fibrations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914056318746624 |
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| author | Birkar, Caucher Qu, Santai |
| author_facet | Birkar, Caucher Qu, Santai |
| contents | 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 $d,t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stein degree on log Calabi-Yau fibrations Birkar, Caucher Qu, Santai Algebraic Geometry 14B05, 14D06, 14J27, 14J45, 14M25 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 $d,t$. |
| title | Stein degree on log Calabi-Yau fibrations |
| topic | Algebraic Geometry 14B05, 14D06, 14J27, 14J45, 14M25 |
| url | https://arxiv.org/abs/2509.20948 |