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arXiv · 2607.05839

Singular fibers of elliptic fibrations on normal $K3$ surfaces

Taro Hayashi·Kazuki Utsumi
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Abstract

We study singular fibers of elliptic fibrations on normal \(K3\) surfaces. For a normal \(K3\) surface \(Y\) with minimal resolution \(ν\colon X \to Y\), we describe singular fibers on \(Y\) in terms of contractions of suitable ADE configurations of \((-2)\)-curves in singular fibers on \(X\). We determine ADE configurations occurring in singular fibers and describe fibers obtained after contraction. As a consequence, we obtain a description of singular fibers of elliptic fibrations on normal \(K3\) surfaces.

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Taro Hayashi, Kazuki Utsumi. 2026-07-07. Singular fibers of elliptic fibrations on normal $K3$ surfaces. https://arxiv.org/abs/2607.05839

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