Fields of moduli of hyperelliptic curves

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Let F be an algebraically closed field with char(F) not equal to 2, let F/K be a Galois extension, and let X be a hyperelliptic curve defined over F. Let ιbe the hyperelliptic involution of X. We show that X can be defined over its field of moduli relative to the extension F/K if Aut(X)/<ι> is not cyclic. We construct explicit examples of hyperelliptic curves not definable over their field of moduli when Aut(X)/<ι> is cyclic.
14 pages

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Number Theory, Algebraic Geometry, 11G99;14H99

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http://salesiana.dossiersoluciones.com/handle/123456789/71792

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407088
 http://arxiv.org/abs/math/0407088

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arXiv