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Non-hyperelliptic Riemann surfaces with real field of moduli but not definable over the reals

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An Erratum to this article was published on 15 May 2012

Abstract

The known examples of explicit equations for Riemann surfaces whose field of moduli is different from their field of definition, are all hyperelliptic. In this paper we construct a family of equations for non-hyperelliptic Riemann surfaces, each of them is isomorphic to its conjugate Riemann surface, but none of them admit an anticonformal automorphism of order 2; that is, each of them has its field of moduli, but not a field of definition, contained in \({{\mathbb R}}\) . These appear to be the first explicit such examples in the non-hyperelliptic case.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Técnica Federico Santa María, Valparaíso, Chile

    Rubén A. Hidalgo

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  1. Rubén A. Hidalgo
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Correspondence to Rubén A. Hidalgo.

Additional information

Partially supported by projects Fondecyt 1070271 and UTFSM 12.09.02.

An erratum to this article can be found at http://dx.doi.org/10.1007/s00013-012-0378-y

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Hidalgo, R.A. Non-hyperelliptic Riemann surfaces with real field of moduli but not definable over the reals. Arch. Math. 93, 219–224 (2009). https://doi.org/10.1007/s00013-009-0025-4

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  • DOI: https://doi.org/10.1007/s00013-009-0025-4

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