On Baer cones in PG(3, q)

Recently, in Innamorati and Zuanni (J. Geom 111:45, 2020. https://doi.org/10.1007/s00022-020-00557-0) the authors give a characterization of a Baer cone of PG(3, q2), q a prime power, as a subset of points of the projective space intersected by any line in at least one point and by every plane in q2 + 1, q2 + q + 1 or q3 + q2 + 1 points. In this paper, we show that a similar characterization holds even without assuming that the order of the projective space is a square, and weakening the assumptions on the three intersection numbers with respect to the planes.