具有唯一奇点和最大代数重数的射影叶状结构
Projective Foliations with a Unique Singular Point and Maximum Algebraic Multiplicity
AI总结：
本文研究复射影平面上具有唯一奇点的余维一全纯叶状结构，聚焦次数为$d$且奇点最大重数为$d$的叶状结构，明确描述该类结构、刻画具唯一奇点的叶状结构，并给出其希尔伯特-芒福德稳定性的相关结果。
AI中文摘要：
对复射影平面$\boldsymbol{\text{CP}}^2$上具有唯一奇点的余维一全纯叶状结构的研究，因与多个重要问题相关而受到日益关注。本文聚焦次数为$d$且具有最大重数$d$的奇点的全纯叶状结构，明确描述该类叶状结构并刻画其中具有唯一奇点的叶状结构，还给出关于这些叶状结构的希尔伯特-芒福德稳定性的若干结果。
英文摘要：
The study of codimension-one holomorphic foliations on the projective plane $\mathbb{CP}^{2}$ with a unique singular point has attracted increasing interest because of its connections with several important problems. In this paper, we focus on holomorphic foliations of degree $d$ having a singular point of maximal multiplicity $d$. We describe explicitly the foliations in this class and characterize those having a unique singular point. We also state some results concerning Hilbert-Mumford stability for these foliations.
