论文标题
关于尖曲线的模量空间的不合理性
On the unirationality of moduli spaces of pointed curves
论文作者
论文摘要
We show that $\mathcal{M}_{g,n}$, the moduli space of smooth curves of genus $g$ together with $n$ marked points, is unirational for $g=12$ and $2 \leq n\leq 4$ and for $g=13$ and $1 \leq n \leq 3$, by constructing suitable dominant families of projective curves in $ \ mathbb {p}^1 \ times \ mathbb {p}^2 $和$ \ mathbb {p}^3 $。我们还为$ g $属的平滑曲线以及$ n $无序的积分的模量曲线展示了几个新的不合理结果，以$ g = 11，n = 7 $和$ g = 12，n = 5,6 $确定其Unirationality。
We show that $\mathcal{M}_{g,n}$, the moduli space of smooth curves of genus $g$ together with $n$ marked points, is unirational for $g=12$ and $2 \leq n\leq 4$ and for $g=13$ and $1 \leq n \leq 3$, by constructing suitable dominant families of projective curves in $\mathbb{P}^1 \times \mathbb{P}^2$ and $\mathbb{P}^3$ respectively. We also exhibit several new unirationality results for moduli spaces of smooth curves of genus $g$ together with $n$ unordered points, establishing their unirationality for $g=11, n=7$ and $g=12, n =5,6$.
