Stacky Framework for the Classification of Singular Fibers in Fibered Surfaces

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 ${\bar{\mathcal{M}}}_g$ 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.