Fields of Moduli of Hyperelliptic Curves

• Autores: Bonnie Huggins
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 2, 2007, págs. 249-262
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n2.a8
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• Resumen

  • Let $X$ be a hyperelliptic curve defined over a field $K$ of characteristic not equal to $2$. Let $\iota$ be the hyperelliptic involution of $X$. We show that $X$ can be defined over its field of moduli if $\Aut(X)/\langle \iota\rangle$ is not cyclic. We construct explicit examples of hyperelliptic curves not definable over their field of moduli when $\Aut(X)/\langle \iota\rangle$ is cyclic.