Stacky Framework for the Classification of Singular Fibers in Fibered Surfaces

2026/07/21 by Javier Reyes
Mathematics · #math.AG

paper · pdf

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 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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