AI 中文总结
该研究针对复射影平面上点的希尔伯特概型，以$d=2$次全纯叶状结构对应的7个点的希尔伯特函数为对象分析覆盖该概型的仿射簇，同时给出$d=3$次的相关结果，是相关领域的初步探索。
AI 中文摘要
复射影平面$\boldsymbol{\text{CP}}^{2}$上具有孤立奇点的$d$次全纯叶状结构由其奇异子概型确定，这些奇异子概型对应$N=d^2+d+1$个点的希尔伯特概型中的元素。本文分析由$N=7$的分划参数化的仿射簇，这些仿射簇覆盖7个点的希尔伯特概型，且其中元素的希尔伯特函数对应$d=2$次全纯叶状结构的希尔伯特函数。此外，本文给出了$d=3$次的若干结果。
英文摘要
The holomorphic foliations of degree $d$ on $\mathbb{CP}^{2}$ with isolated singularities are determined by their singular subschemes, which correspond to elements in the Hilbert Scheme of $N=d^{2}+d+1$ points. In this paper, we analyze the affine varieties parametrized by a partition of $N=7$ that cover the Hilbert Scheme of seven points, with the property that the Hilbert function of the elements in these affine varieties corresponds to that of holomorphic foliation of degree $d=2$. Moreover, we present some results for degree $3$.
