AI 中文总结
研究亏格为六的曲线的模域问题，通过考虑模空间\(M_6\)的分层，探讨曲线在其模域上有模型的条件。
AI 中文摘要
在代数闭域\(K\)上，簇\(X\)的模域定义为\(K\)中使\(X\cong X^{\sigma}\)的自同构\(\sigma\)的固定域。一个基本问题是在何种条件下一个簇在其模域上有一个模型。我们通过考虑模空间\(M_6\)的分层来研究亏格为\(6\)的曲线的这个问题。
英文摘要
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 $X\cong X^σ$. 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 $M_6$.
