Fields of moduli and fields of definition of curves

Abstract

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.

UC Berkeley Ph.D. thesis, 168 pages

References in corpus (3)

• Field of moduli and field of definition for curves of genus 2
• Finiteness results for modular curves of genus at least 2
• Fields of Definition of Rational Points on Varieties

Cited by in corpus (4)

• Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields
• Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group
• Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent
• Computing twists of hyperelliptic curves