On the Fields of Moduli of Curves of Genus Six

2026/07/21 by Tianzhi Yang
Mathematics · #math.AG

paper · pdf

Abstract

The field of moduli of a variety X over an algebraically closed field K is defined as the fixed field of those automorphisms σ of K for which X≅ X^σ. A fundamental question is under what conditions a variety admits a model over its field of moduli. We investigate this problem for curves of genus 6, by considering the stratification of the moduli space M₆.

Related

• Fields of Moduli of Smooth del Pezzo Surfaces
• A census of genus 6 curves over \mathbbF₂
• Field of moduli and field of definition for curves of genus 2
• Sur le corps des modules de certaines variétés
• Fields of moduli and the arithmetic of tame quotient singularities