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Fields of moduli of hyperelliptic curves

Bonnie Huggins
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Abstract

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.

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Bonnie Huggins. 2004-07-06. Fields of moduli of hyperelliptic curves. https://arxiv.org/abs/math/0407088

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