Reduction of the Hurwitz space of metacyclic covers

Details Reduction of the Hurwitz space of metacyclic covers Reduction of the Hurwitz space of metacyclic covers

2002-04-03

arxiv.org/abs/math/0204043v1

Mathematics

Algebraic Geometry

25 pages, 3 figures

Scientific paper

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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