Fields of moduli of hyperelliptic curves
Number Theory
2007-05-23 v1 Algebraic Geometry
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 \iota be 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)/<\iota> is not cyclic. We construct explicit examples of hyperelliptic curves not definable over their field of moduli when Aut(X)/<\iota> is cyclic.
Cite
@article{arxiv.math/0407088,
title = {Fields of moduli of hyperelliptic curves},
author = {Bonnie Huggins},
journal= {arXiv preprint arXiv:math/0407088},
year = {2007}
}
Comments
14 pages