The stack of Potts curves and its fibre at a prime of wild ramification

In this note we study the modular properties of a family of cyclic coverings of of degree N, in all odd characteristics. We compute the moduli space of the corresponding algebraic stack over , as well as the Picard groups over algebraically closed fields. We put special emphasis on the study of the fibre of the stack at a prime of wild ramification; in particular we show that the moduli space has good reduction at such a prime.