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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some $ 4$-point Hurwitz numbers in positive characteristic


Authors: Irene I. Bouw and Brian Osserman
Journal: Trans. Amer. Math. Soc. 363 (2011), 6685-6711
MSC (2010): Primary 11G20, 14D15, 14H37
Published electronically: June 15, 2011
MathSciNet review: 2833573
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Abstract: In this paper, we compute the number of covers of curves with given branch behavior in characteristic $ p$ for one class of examples of genus 0, 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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Additional Information

Irene I. Bouw
Affiliation: Department of Mathematics, University of Ulm, 89069 Ulm, Germany
Email: irene.bouw@uni-ulm.de

Brian Osserman
Affiliation: Department of Mathematics, University of California at Davis, Davis, California 95616
Email: osserman@math.ucdavis.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05347-X
PII: S 0002-9947(2011)05347-X
Received by editor(s): June 9, 2009
Received by editor(s) in revised form: January 18, 2010, and March 11, 2010
Published electronically: June 15, 2011
Article copyright: © Copyright 2011 American Mathematical Society