arXiv:2103.00537 Abstract | arXiv Analytics

arXiv:2103.00537 [math.DS]Abstract References Reviews Resources

Foliations on $\mathbb{P}^2$ with only one singular point

Percy Fernández, Liliana Puchuri, Rudy Rosas

Published 2021-02-28Version 1

In this paper we study holomorphic foliations on $\mathbb{P}^2$ with only one singular point. If the singularity has algebraic multiplicity one, we prove that the foliation has no invariant algebraic curve. We also present several examples of such foliations in degree three.

Comments: 17 pages

Categories: math.DS

Subjects: 37F75, 32S65, 32M25

Keywords: singular point, invariant algebraic curve, study holomorphic foliations, algebraic multiplicity, singularity

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