Fields of moduli and fields of definition of curves

Bonnie Huggins

Fields of moduli and fields of definition of curves

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arxiv math/0610247 v1 pith:ZN7H4KJV submitted 2006-10-07 math.NT math.AG

Fields of moduli and fields of definition of curves

Bonnie Huggins This is my paper

classification math.NT math.AG

keywords fieldsmodulicurvesfieldcharacteristicconditionscurvedefinable

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We determine conditions that guarantee that a hyperelliptic or plane curve over a field of characteristic not equal to 2 can be defined over its field of moduli. We also give new examples of curves not definable over their fields of moduli.

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On the Fields of Moduli of Curves of Genus Six
math.AG 2026-07 conditional novelty 7.0

For genus-6 curves, bielliptic curves descend to their field of moduli, and non-descent can only occur for curves on smooth degree-5 del Pezzo surfaces with automorphism group C2 or D10 (with √-1 outside the base fiel...