A pencil of plane curves determines a foliation on the projective plane which, generically, has exactly $d^2$ radial singularities, and apart from these singularities, the foliation is locally given by closed holomorphic 1-forms. In this talk, we will prove the converse statement: a foliation of degree $2d-2$ on the projective plane with singularities of this type, under generic conditions, is determined by a pencil of curves. In other words, every degree $d$ curve passing by the radial singularities is invariant. In order to do that, we will introduce the notion of flat partial connections and relate the existence of flat meromorphic extensions of a flat partial connections with the existence of invariant curves.