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

DOI10.1007/S10711-022-00724-4arXiv2103.00537MaRDI QIDQ6361749

Rudy Rosas, Percy Fernández, Liliana Puchuri

Publication date: 28 February 2021

Abstract: 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.

Mathematics Subject Classification ID

Germs of analytic sets, local parametrization (32B10) Singularities of holomorphic vector fields and foliations (32S65) Dynamical aspects of holomorphic foliations and vector fields (37F75)

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