AI 中文总结
本工作将$G_n^k$理论推广到任意超图，结合球形辫子的模空间分层研究相关群的映射性质，并提出其在阿贝尔簇上适用性的待解决问题。
AI 中文摘要
本工作将$G_n^k$理论推广到任意超图的情况，针对球形辫子的情况单独进行研究，使用模空间$\boldsymbol{\textit{M}}_n(S^2)$的分层及编码射影约束的超图$\boldsymbol{\textit{\u0393}}_n^{\text{sph}}$。与原始$G_{n}^{k}$理论中由恰好$k$个粒子决定余维-1性质不同，本工作考虑对应余维-1分层的各种情况。这些群可良好地映射到循环群的自由积。在未解决问题中，重点关注上述构造对阿贝尔簇、特别是椭圆曲线的适用性问题。
英文摘要
In this work, we construct a generalization of the $G_n^k$-theory to the case of an arbitrary hypergraph. The case of spherical braids is considered separately, using the stratification of the moduli space $\mathcal{M}_n(S^2)$ and the hypergraph $Γ_n^{\mathrm{sph}}$ encoding projective constraints. In contrast to the original $G_{n}^{k}$ theory, where codimension-one properties are determined by exactly $k$ particles, the present work considers various cases corresponding to strata of codimension~$1$. These groups admit nice maps to free products of cyclic groups. Among unsolved problems, we emphasize the question how the above construction works for abelian varieties and, in particular, for elliptic curves.
Comments9 pages
