Abstract.
In this paper, for all genera g>1, g ≡ 1 mod 4, we construct an explicit hyperelliptic curve whose field of moduli is \( \mathbb{Q} \)and such that the minimum subfield of \( \mathbb{R} \) over which it can be hyperelliptically defined is a degree three extension of \( \mathbb{Q} \). These examples are related to previous work by Earle, Shimura, and Mestre and to a recent conjecture by Shaska.
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Received: 19 January 2005
An erratum to this article is available at http://dx.doi.org/10.1007/s00013-013-0582-4.
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Fuertes, Y., González-Diez, G. Fields of moduli and definition of hyperelliptic covers. Arch. Math. 86, 398–408 (2006). https://doi.org/10.1007/s00013-005-1433-8
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DOI: https://doi.org/10.1007/s00013-005-1433-8