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Fields of moduli and definition of hyperelliptic curves of odd genus

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Abstract

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 \({\mathbb{Q}}\).

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  1. Departamento de Matemáticas, U. Autónoma de Madrid, 28049, Madrid, Spain

    Yolanda Fuertes

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  1. Yolanda Fuertes
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Correspondence to Yolanda Fuertes.

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Fuertes, Y. Fields of moduli and definition of hyperelliptic curves of odd genus. Arch. Math. 95, 15–18 (2010). https://doi.org/10.1007/s00013-010-0138-9

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  • DOI: https://doi.org/10.1007/s00013-010-0138-9

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