带点曲线模空间的上同调
Cohomology of moduli spaces of pointed curves
浏览论文内容
中文总结 AI 辅助
本文延续相关文献研究带点曲线模空间的上同调，证明了任意光滑射影曲线$C$上$n$个有序不同点空间的Fulton-MacPherson紧化$C[n]$的贝蒂数分布随$n$趋于无穷呈渐近高斯分布。
中文摘要 AI 辅助
本文在回顾$\boldsymbol{\bar{\boldsymbol{\textit{\textbf{M}}}}}_{\boldsymbol{0,n}}$上同调的最新进展后，延续文献[2,4,5,6,7,8]进一步研究带点曲线模空间的上同调；特别地，证明了任意光滑射影曲线$C$上$n$个有序不同点空间的Fulton-MacPherson紧化$C[n]$的贝蒂数分布，当$n$趋于无穷时呈渐近高斯分布。
英文摘要
In this paper, after reviewing recent progress on the cohomology of $\overline{\cal M}_{0,n}$, we further our investigation on the cohomology of moduli spaces of pointed curves in continuation of [2,4,5,6,7,8]. In particular, we prove that the Betti number distribution of the Fulton-MacPherson compactification $C[n]$ of the space of $n$ ordered distinct points on any smooth projective curve $C$ is asymptotically Gaussian as $n$ goes to infinity.
