论文标题
除法曲线的模量领域
The field of moduli of a divisor on a rational curve
论文作者
论文摘要
令$ k $为一个具有代数闭合$ \ bar {k} $和$ d \ subset \ mathbb {p}^{1} _ {\ bar {k}} $的字段。 A. Marinatto证明，当$ n $奇怪或$ n = 4 $，$ d $时，$ \ mathbb {p}^{1} _ {k（d）} $上的除数。 我们完全分析了$ d $何时在$ k（d）$上平滑，投影属$ 0 $ 0 $ 0 $ 0 $ 0 $ 0的问题，可能没有合理的积分。特别是，我们甚至研究了剩下的情况$ n \ ge 6 $，并且我们获得了Marinatto的结果和B. Huggins定理的概念证明，内容涉及过度纤维化曲线模量领域。
Let $k$ be a field with algebraic closure $\bar{k}$ and $D \subset \mathbb{P}^{1}_{\bar{k}}$ a reduced, effective divisor of degree $n \ge 3$, write $k(D)$ for the field of moduli of $D$. A. Marinatto proved that when $n$ is odd, or $n = 4$, $D$ descends to a divisor on $\mathbb{P}^{1}_{k(D)}$. We analyze completely the problem of when $D$ descends to a divisor on a smooth, projective curve of genus $0$ on $k(D)$, possibly with no rational points. In particular, we study the remaining cases $n \ge 6$ even, and we obtain conceptual proofs of Marinatto's results and of a theorem by B. Huggins about the field of moduli of hyperelliptic curves.
