A curve algebraically but not rationally uniformized by radicals
Algebraic Geometry
2010-03-26 v1 Group Theory
Abstract
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.
Cite
@article{arxiv.math/0407194,
title = {A curve algebraically but not rationally uniformized by radicals},
author = {Gian Pietro Pirola and Enrico Schlesinger},
journal= {arXiv preprint arXiv:math/0407194},
year = {2010}
}
Comments
8 pages, AMSlatex