Stacky Framework for the Classification of Singular Fibers in Fibered Surfaces

Javier Reyes

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arXiv · 2607.19347

Stacky Framework for the Classification of Singular Fibers in Fibered Surfaces

Javier Reyes

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Abstract

We develop a strategy for the classification of singular fibers in smooth fibered surfaces by exploiting the fact that, in the tame case, a fibration with smooth general fiber of genus $g > 1$ corresponds to a representable morphism from a stacky base to $\overline{\mathcal{M}}_g$ thanks to the root stack valuative criterion for properness of tame stacks. This framework serves as another justification of Dokchitser's classification of reduction types independently of Winters' abstract result.

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Javier Reyes. 2026-07-21. Stacky Framework for the Classification of Singular Fibers in Fibered Surfaces. https://arxiv.org/abs/2607.19347

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