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arXiv · 1003.4829

A New Curve Algebraically but not Rationally Uniformized by Radicals

Gian Pietro Pirola·Cecilia Rizzi·Enrico Schlesinger
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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.

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Gian Pietro Pirola, Cecilia Rizzi, Enrico Schlesinger. 2010-03-25. A New Curve Algebraically but not Rationally Uniformized by Radicals. https://arxiv.org/abs/1003.4829

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