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A TOWER OF RIEMANN SURFACES WHICH CANNOT BE DEFINED OVER THEIR FIELD OF MODULI

Part of: Riemann surfaces

Published online by Cambridge University Press:  10 June 2016

MICHELA ARTEBANI ,
MARIELA CARVACHO ,
RUBEN A. HIDALGO  and
SAÚL QUISPE
MICHELA ARTEBANI
Affiliation:
Departamento de Matemática, Universidad de Concepción., Casilla 160-C, Concepción, Chile e-mail: martebani@udec.cl
MARIELA CARVACHO
Affiliation:
Departamento de Matemática, Universidad Técnica Federico Santa María., Casilla 110-V, Valparaíso, Chile e-mail: mariela.carvacho@usm.cl
RUBEN A. HIDALGO
Affiliation:
Departamento de Matemática y Estadística, Universidad de La Frontera., Casilla 54-D, Temuco, Chile e-mails: ruben.hidalgo@ufrontera.cl, saul.quispe@ufrontera.cl
SAÚL QUISPE
Affiliation:
Departamento de Matemática y Estadística, Universidad de La Frontera., Casilla 54-D, Temuco, Chile e-mails: ruben.hidalgo@ufrontera.cl, saul.quispe@ufrontera.cl
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Abstract

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Explicit examples of both hyperelliptic and non-hyperelliptic curves which cannot be defined over their field of moduli are known in the literature. In this paper, we construct a tower of explicit examples of such kind of curves. In that tower there are both hyperelliptic curves and non-hyperelliptic curves.

MSC classification

Primary: 30F10: Compact Riemann surfaces and uniformization
Secondary: 30F20: Classification theory of Riemann surfaces 30F40: Kleinian groups
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 2 , May 2017 , pp. 379 - 393
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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