Archiv der Mathematik

, Volume 95, Issue 1, pp 15–18 | Cite as

Fields of moduli and definition of hyperelliptic curves of odd genus

  • Yolanda Fuertes


Mestre has shown that if a hyperelliptic curve C of even genus is defined over a subfield \({k \subset \mathbb{C}}\) then C can be hyperelliptically defined over the same field k. In this paper, for all genera g > 1, \({g\equiv1}\) mod 4, hence odd, we construct an explicit hyperelliptic curve defined over \({\mathbb{Q}}\) which can not be hyperelliptically defined over \({\mathbb{Q}}\).

Mathematics Subject Classification (2000)

14H37 14H45 14G99 


Hyperelliptic curves Automorphisms Field of moduli Field of definition 


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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Departamento de MatemáticasU. Autónoma de MadridMadridSpain

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