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

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.

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Correspondence to Liliana Puchuri.

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Fernández, P., Puchuri, L. & Rosas, R. Foliations on \(\mathbb {P}^2\) with only one singular point. Geom Dedicata 216, 59 (2022). https://doi.org/10.1007/s10711-022-00724-4

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  • DOI: https://doi.org/10.1007/s10711-022-00724-4

Keywords

  • Holomorphic Foliations
  • Indices of Vector Fields
  • Invariant Algebraic Curve

Mathematics Subject Classification (2020)

  • 37F75
  • 32S65
  • 32B10