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arXiv · 2603.02347

Kodaira-type classification of singular fibers of some minimal abelian fibrations

Yoon-Joo Kim
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Abstract

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.

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Yoon-Joo Kim. 2026-03-02. Kodaira-type classification of singular fibers of some minimal abelian fibrations. https://arxiv.org/abs/2603.02347

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