A characterization of the family of secant lines to a hyperbolic quadric in PG(3,q), q odd, Part II

Abstract

In [9], two of us classified line sets in PG(3, q), q odd, that satisfy a certain list of properties. It was shown there that if q >= 7, then each such line set is either the set of secant lines with respect to a hyperbolic quadric of PG(3, q) or belongs to a certain "hypothetical family" of line sets (for which no examples were known in [9]). In the present paper, we achieve two goals. On the one hand, we extend the mentioned classification result to all odd prime powers q. On the other hand, we study the hypothetical family of line sets and show that they are related to quadratic sets of the Klein quadric. This will allow us to show that such line sets exist for every odd prime power q.(c)