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arXiv · 2607.18992

On the Fields of Moduli of Curves of Genus Six

Tianzhi Yang
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Abstract

The field of moduli of a variety $X$ over an algebraically closed field $K$ is defined as the fixed field of those automorphisms $\sigma$ of $K$ for which $X\cong X^{\sigma}$. 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 $M_6$.

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Tianzhi Yang. 2026-07-21. On the Fields of Moduli of Curves of Genus Six. https://arxiv.org/abs/2607.18992

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