Abstract. In this talk we will focus on semicomplete Halphen vector fields.
It is shown that rational semicomplete Halphen vector fields are in ``one-to-one'' correspondence with singular uniformizable projective structures on compact Riemann surfaces.
In turn, many examples of the projective structures in question can be obtained by means of Teichmüller space techniques or, more precisely, from Bers simultaneous uniformization theorem.
The proof of this correspondence is the main topic for this discussion.