Stacky Framework for the Classification of Singular Fibers in Fibered Surfaces

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.

arXiv comment48 pages, comments welcome