Galois branched covers with fixed ramification locus

2013/10/16 by Ryan Eberhart, Eberhart, Ryan
Mathematics · #12F10 #14D05 #14L30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:12F10 #msc:14D05 #msc:14L30

paper · pdf · doi:10.48550/arxiv.1310.4245

14 pages

arxiv created 2013/10/16 · arxiv updated 2013/10/17

Abstract

We examine conditions under which there exists a non-constant family of Galois branched covers of curves over an algebraically closed field k of fixed degree and fixed ramification locus, under a notion of equivalence derived from considering linear series on a fixed smooth proper source curve X. We show such a family exists precisely when the following conditions are satisfied: char(k)=p>0, X is isomorphic to ℙ¹_k, there is a unique ramification point, and the Galois group is (ℤ/pℤ)^m for some integer m>0.

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