On the Classification of Foliations by Curves with Curve Singularities

In this talk, I will discuss the classification problem for holomorphic foliations by curves on projective three-space whose singular scheme contains a curve, under the assumption that the canonical bundle of the foliation has low degree. Particular attention will be given to the structure of the corresponding moduli spaces and to the way in which these spaces are governed by numerical invariants of the singular curve and of the conormal sheaf of the foliation. This is joint work with Marcos Jardim and Simone Marchesi.