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Paper detail

A New Curve Algebraically but not Rationally Uniformized by Radicals

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.

preprint2010arXivOpen access
Gian Pietro PirolaCecilia RizziEnrico Schlesinger
math.AG
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Gian Pietro PirolaCecilia RizziEnrico Schlesinger

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