Open Access
January 2014 A new curve algebraically but not rationally uniformized by radicals
Gian PietroI Pirola, Cecilia Rizzi, Enrico Schlesinger
Asian J. Math. 18(1): 127-142 (January 2014).


We give a new example of a curve $C$ algebraically, but not rationally, uniformized by radicals. This means that $C$ has no map onto $\mathbb{P}^1$ with solvable Galois group, while there exists a curve $C'$ that maps onto $C$ and has a finite morphism to $\mathbb{P}^1$ 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 PietroI Pirola. Cecilia Rizzi. Enrico Schlesinger. "A new curve algebraically but not rationally uniformized by radicals." Asian J. Math. 18 (1) 127 - 142, January 2014.


Published: January 2014
First available in Project Euclid: 27 August 2014

zbMATH: 1295.81135
MathSciNet: MR3215343

Primary: 14H10 , 14H30 , 20B25

Keywords: Galois groups , Monodromy groups , projective curves

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 1 • January 2014
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