Characterization of families of lines Meeting a Hermitian variety of PG(3, Q2) in Q + 1 points

Abstract

In this study, we undertake a detailed classification of families of lines in the three-dimensional projective space PG(3, q2) that fulfill a prescribed set of incidence conditions. Our investigation reveals that such line families can be precisely characterized in two distinct ways. Specifically, we demonstrate that these families either correspond to the set of all lines intersecting a Hermitian variety of PG(3, q2) in exactly q + 1 points, or they form part of a certain conjectural or “hypothetical” configuration of line sets exhibiting analogous geometric behavior. This classification provides deeper insight into the incidence structure of Hermitian varieties and contributes to a broader understanding of line geometries in finite projective spaces.