Ruben A. Hidalgo, Yolanda Fuertes
Published 2012-05-29, updated 2012-05-31Version 2
It has been conjectured that every algebraic curve may be defined either over its field of moduli or over an extension of degree two of it. In this paper we provide a negative answer to it by giving examples of hyperelliptic curves which cannot be defined over an extension of degree at least two over their fields of moduli.
Comments: This paper has been withdrawn by the author due to a crucial error in the provided example
Large $3$-groups of automorphisms of algebraic curves in characteristic $3$
Algebraic curves with many automorphisms
On large automorphism groups of algebraic curves in positive characteristic
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