Affine sets arising from spreads (Q1022869)

There exists a bijective correspondence between spreads of PG\((3,q)\) and ovoids of the Klein quadric \(Q^ +(5,q)\). Let \(\mathbb O\) be an ovoid of \(Q^ +(5,q)\) and let \(x \in \mathbb O\), then the image of \(\mathbb O \setminus \{x\}\) under stereographic projection from \(x\) is called an affine set. The authors investigate properties of affine sets, especially those associated with symplectic spreads. In particular, they show that the Lüneburg spreads admit affine sets which are disjoint unions of \(q\)-arcs, each of which can be completed to a translation hyperoval.