Linear series and existence of branched covers

Details Linear series and existence of branched covers Linear series and existence of branched covers

2005-07-05

arxiv.org/abs/math/0507096v2

Mathematics

Algebraic Geometry

19 pages. Heavily revised. Non-sharp existence results removed, many examples added, and main theorem stated in stronger form

Scientific paper

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 existence and non-existence of branched covers of the projective line in positive characteristic. Our results are both in terms of ramification indices and the sharper invariant of monodromy groups, and the first class of results are obtained by intrinsically algebraic and positive-characteristic arguments.

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