A curve algebraically but not rationally uniformized by radicals

Details A curve algebraically but not rationally uniformized by radicals A curve algebraically but not rationally uniformized by radicals

2004-07-12

arxiv.org/abs/math/0407194v1

J. Algebra 289 (2005), no. 2, 412--420.

Mathematics

Algebraic Geometry

8 pages, AMSlatex

Scientific paper

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.

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