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Linear series and the existence of branched covers

Part of: Curves

Published online by Cambridge University Press:  01 January 2008

Brian Osserman
Brian Osserman*
Affiliation:
Department of Mathematics, University of California at Davis, One Shields Ave., Davis, CA 95616, USA (email: [email protected])
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Abstract

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In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on the existence and non-existence of tamely branched covers of the projective line in positive characteristic. Our results are both in terms of ramification indices and the sharper invariant of monodromy cycles, and the first class of results are obtained by intrinsically algebraic and positive-characteristic arguments.

Keywords

tame coverslimit linear series

MSC classification

Secondary: 14H30: Coverings, fundamental group
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 1 , January 2008 , pp. 89 - 106
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

The author was supported by fellowships from the Japan Society for the Promotion of Science and the NSF.