A New Curve Algebraically but not Rationally Uniformized by Radicals

Details A New Curve Algebraically but not Rationally Uniformized by Radicals A New Curve Algebraically but not Rationally Uniformized by Radicals

2010-03-25

arxiv.org/abs/1003.4829v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

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.

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