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 $${{\mathbb {C}}}{{\mathbb {P}}}^2$$ C P 2 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.