Abstract
Zariski proved the general complex projective curve of genus g > 6 is not rationally uniformized by radicals, that is, admits no map to P 1 whose Galois group is solvable. We give an example of a genus seven 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
