Kodaira-type classification of singular fibers of some minimal abelian fibrations
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911481085296640 |
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| author | Kim, Yoon-Joo |
| author_facet | Kim, Yoon-Joo |
| contents | Let $X \to S$ be a minimal abelian fibration of relative dimension $n$ over a curve. We classify all possible singular fibers $X_s$ having $(n-1)$-dimensional ``abelian variety parts''. This generalizes Kodaira's work on elliptic fibrations, and Matsushita and Hwang--Oguiso's work on Lagrangian fibrations into a single framework. The classification is divided into three parts: semistable, unstable, and multiple. Multiple fibers are again divided into three types: semistable-like, mixed, and unstable-like. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02347 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kodaira-type classification of singular fibers of some minimal abelian fibrations Kim, Yoon-Joo Algebraic Geometry Let $X \to S$ be a minimal abelian fibration of relative dimension $n$ over a curve. We classify all possible singular fibers $X_s$ having $(n-1)$-dimensional ``abelian variety parts''. This generalizes Kodaira's work on elliptic fibrations, and Matsushita and Hwang--Oguiso's work on Lagrangian fibrations into a single framework. The classification is divided into three parts: semistable, unstable, and multiple. Multiple fibers are again divided into three types: semistable-like, mixed, and unstable-like. |
| title | Kodaira-type classification of singular fibers of some minimal abelian fibrations |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2603.02347 |