论文标题
$ \ overline {\ mathcal {m}} _ {0，n} $的同谋的表示形式
Representations on the cohomology of $\overline{\mathcal{M}}_{0,n}$
论文作者
论文摘要
Moduli空间$ \ OVILLINE {\ MATHCAL {M}} _ {0，n} $ $ n $尖的稳定曲线属的属$ 0 $允许对称组$ s_n $的动作，并通过定位点数。我们为$ \ overline {\ Mathcal {m}} _ {0，n} $的同时组中的$ s_n $ Action的字符提供了封闭公式。这是通过研究清单的模量空间的墙壁交叉口来实现的，这些墙壁可为我们提供$ \ overline {\ Mathcal {m}} _ {0，n} $的新电感构造，相对于对称组动作。此外，我们证明了$ h^{2k}（\ overline {\ mathcal {m}} _ {0，n}）$ for $ k \ le 3 $和$ h^{2k}（\ overline {\ nathcal {\ Mathcal {m}}}} _ {0，n} _ {0，n}） h^{2k-2}（\ edimline {\ Mathcal {m}} _ {0，n}）$对于任何$ k $都是置换表示形式。我们的方法也适用于相关的模块空间，我们为Fulton-Macpherson紧凑型共同体的$ s_n $ - 代表性的特征提供了一个封闭式公式。 $ \ OVILLINE {\ MATHCAL {M}} _ {0，N}（\ Mathbb {p}^{M-1}，1）$稳定地图的$。
The moduli space $\overline{\mathcal{M}}_{0,n}$ of $n$ pointed stable curves of genus $0$ admits an action of the symmetric group $S_n$ by permuting the marked points. We provide a closed formula for the character of the $S_n$-action on the cohomology of $\overline{\mathcal{M}}_{0,n}$. This is achieved by studying wall crossings of the moduli spaces of quasimaps which provide us with a new inductive construction of $\overline{\mathcal{M}}_{0,n}$, equivariant with respect to the symmetric group action. Moreover we prove that $H^{2k}(\overline{\mathcal{M}}_{0,n})$ for $k\le 3$ and $H^{2k}(\overline{\mathcal{M}}_{0,n})\oplus H^{2k-2}(\overline{\mathcal{M}}_{0,n})$ for any $k$ are permutation representations. Our method works for related moduli spaces as well and we provide a closed formula for the character of the $S_n$-representation on the cohomology of the Fulton-MacPherson compactification $\mathbb{P}^1[n]$ of the configuration space of $n$ points on $\mathbb{P}^1$ and more generally on the cohomology of the moduli space $\overline{\mathcal{M}}_{0,n}(\mathbb{P}^{m-1},1)$ of stable maps.
