Reduction of the Hurwitz space of metacyclic covers
Irene I. Bouw
Abstract
We compute the stable reduction of some Galois covers of the projective line branched at three points. These covers are constructed using Hurwitz spaces parameterizing metacyclic covers. The reduction is determined by a hypergeometric differential equation. This generalizes the result of Deligne- Rapoport on the reduction of the modular curve X(p).
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