A curve algebraically but not rationally uniformized by radicals
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Zariski proved the general complex projective curve of genus g>6 is not rationally uniformized by radicals, that is, admits no map to the projective line whose Galois group is solvable. We give an example of a genus 7 complex projective curve Z that is not rationally uniformized by radicals, but such that there is a finite covering Z' -> Z with Z' rationally uniformized by radicals. The curve providing the example appears in a paper by Debarre and Fahlaoui where a construction is given to show the Brill Noether loci W_d(C) in the Jacobian of a curve C may contain translates of abelian subvarieties not arising from maps from C to other curves.
8 pages, AMSlatex
Coverings of curves, fundamental group, Special algebraic curves and curves of low genus, Algebra and Number Theory, Teoria di Galoi, Projective curves, Group Theory (math.GR), projective curves, monodromy groups, Uniformizzazione, Primitive groups, Mathematics - Algebraic Geometry, Galois groups, Monodromy groups, FOS: Mathematics, 14H10,14H30,20B25, Curve algebriche, Mathematics - Group Theory, Algebraic Geometry (math.AG)
Coverings of curves, fundamental group, Special algebraic curves and curves of low genus, Algebra and Number Theory, Teoria di Galoi, Projective curves, Group Theory (math.GR), projective curves, monodromy groups, Uniformizzazione, Primitive groups, Mathematics - Algebraic Geometry, Galois groups, Monodromy groups, FOS: Mathematics, 14H10,14H30,20B25, Curve algebriche, Mathematics - Group Theory, Algebraic Geometry (math.AG)
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