Foliations on ruled surfaces with invariant sections (Q2747298)

This paper is a contribution to the explicit description of singular holomorphic foliations on ruled surfaces. The paper considers foliations keeping a normalized section of the ruling as an invariant curve, and with one singularity at some point in this section. If the singularity has an invertible linear part, then there are two separatices by the singularity; the invariant section and a second one, which is assumed to be a compact Riemann surface embedded on the ruled surface. Under these assumptions the author gets the existence of five families of foliations. Examples for each family are given.