Baer subplanes generated by collineations between pencils of lines

In this paper we define a degenerateC _F-set in PG (2,q ²) as the set of points of intersection of corresponding lines under a suitable collineation between two pencils of lines with vertices two distinct pointsA andB mapping the lineA ∨B onto itself. We prove that every such a set is the union of the lineA ∨B and a Baer subplane and vice versa every Baer subplane can be seen as a subset of a degenerateC _F-set.