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 Pk1, there is a unique ramification point, and the Galois group is (Z/pZ)m for some integer m>0.
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