Fields of moduli of hyperelliptic curves

By Bonnie Huggins. 2004

50 citations recorded by the source corpus.

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)/ is not cyclic. We construct explicit examples of hyperelliptic curves not definable over their field of moduli when Aut(X)/ is cyclic.

Subfields: Geometry and Topology, Information Systems, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/81e9736038bcb8d16b92d509b9e55685bdc52513

How researchers see this paper

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In Geometry and Topology

1. Christophe Ritzenthaler
2. Reynald Lercier

In Information Systems

1. Christophe Ritzenthaler
2. Reynald Lercier

In Mathematical Physics

1. Christophe Ritzenthaler
2. Reynald Lercier

Citations in the corpus

• Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects (2011, background): “In [29] and [28], the following results are proved.”