We present enumerative results for holomorphic foliations by curves on \(\mathbb {P}^{n}\), n ≥ 3, with singularities of positive dimension. Some of the results presented improve previous ones due to Corrêa et al. (Annales de l’institut Fourier, 64(4):1781–1805, 2014) and Costa (Ann Fac Sci Toulouse, Math (6), 15(2):297–321, 2006). We also present an enumerative result bounding the number of isolated singularities in a projective subvariety invariant by a holomorphic foliation by curves on \(\mathbb {P}^{n}\) with a singularity of positive dimension. Moreover, we construct a family of holomorphic foliations by curves on \(\mathbb {P}^{n}\) with a singularity of a positive dimension where its Milnor number is exhibited.

中文翻译：

---

关于正维奇异性的曲线叶面

我们本枚举结果，用于通过对曲线全纯面理\（\ mathbb {P} ^ {N} \） ，Ñ ≥3，具有正维奇点。由于Corrêa等人的提出，一些结果改进了以前的结果。（Annales de l'institut Fourier，64（4）：1781-1805，2014）和Costa（Ann Fac Sci Toulouse，Math（6），15（2）：297-321，2006）。我们还给出了一个枚举结果，该结果用正维奇异性\（\ mathbb {P} ^ {n} \）上的曲线通过全纯叶形来限定射影子变体不变量中孤立奇异点的数量。此外，我们通过\（\ mathbb {P} ^ {n} \）上的曲线构造一个全同叶系列，其奇异点的Milnor数为正数 展出。