Some 4-point Hurwitz numbers in positive characteristic

Details Some 4-point Hurwitz numbers in positive characteristic Some 4-point Hurwitz numbers in positive characteristic

2009-06-09

arxiv.org/abs/0906.1793v1

Mathematics

Algebraic Geometry

23 pages

Scientific paper

In this paper, we compute the number of covers of curves with given branch behavior in characteristic p for one class of examples with four branch points and degree p. Our techniques involve related computations in the case of three branch points, and allow us to conclude in many cases that for a particular choice of degeneration, all the covers we consider degenerate to separable (admissible) covers. Starting from a good understanding of the complex case, the proof is centered on the theory of stable reduction of Galois covers.

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