Fields of moduli and definition of hyperelliptic curves of odd genus |
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Authors: | Yolanda Fuertes |
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Affiliation: | 1. Departamento de Matem??ticas, U. Aut??noma de Madrid, 28049, Madrid, Spain
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Abstract: | Mestre has shown that if a hyperelliptic curve C of even genus is defined over a subfield k ì mathbbC{k subset mathbb{C}} then C can be hyperelliptically defined over the same field k. In this paper, for all genera g > 1, g o 1{gequiv1} mod 4, hence odd, we construct an explicit hyperelliptic curve defined over mathbbQ{mathbb{Q}} which can not be hyperelliptically defined over mathbbQ{mathbb{Q}}. |
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