Remarks on Foliations on $${{\mathbb {C}}}{{\mathbb {P}}}^2$$ with a Unique Singular Point

Abstract This paper is a contribution to the study of foliations on $${{\mathbb {C}}}{{\mathbb {P}}}^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> with a unique singularity. We provide an explicit example in degree 7 of such a foliation, in the non dicritical case, having a divergent separatrix, and subsequently, we study different families of such foliations in low degree.