A New Curve Algebraically but not Rationally Uniformized by Radicals
Algebraic Geometry
2010-03-26 v1
Abstract
We give a new example of a curve C algebraically, but not rationally, uniformized by radicals. This means that C has no map onto the projective line P^1 with solvable Galois group, while there exists a curve C' that maps onto C and has a finite morphism to P^1 with solvable Galois group. We construct such a curve C of genus 9 in the second symmetric product of a general curve of genus 2. It is also an example of a genus 9 curve that does not satisfy condition S(4,2,9) of Abramovich and Harris.
Keywords
Cite
@article{arxiv.1003.4829,
title = {A New Curve Algebraically but not Rationally Uniformized by Radicals},
author = {Gian Pietro Pirola and Cecilia Rizzi and Enrico Schlesinger},
journal= {arXiv preprint arXiv:1003.4829},
year = {2010}
}
Comments
12 pages