The exterior splash in PG(6,q): Transversals [article]

S.G. Barwick, Wen-Ai Jackson
2014 arXiv   pre-print
Let π be an order-q-subplane of PG(2,q^3) that is exterior to ℓ_∞. Then the exterior splash of π is the set of q^2+q+1 points on ℓ_∞ that lie on an extended line of π. Exterior splashes are projectively equivalent to scattered linear sets of rank 3, covers of the circle geometry CG(3,q), and hyper-reguli in PG(5,q). In this article we use the Bruck-Bose representation in PG(6,q) to investigate the structure of π, and the interaction between π and its exterior splash. In PG(6,q), an exterior
more » ... sh S has two sets of cover planes (which are hyper-reguli) and we show that each set has three unique transversals lines in the cubic extension PG(6,q^3). These transversal lines are used to characterise the carriers of S, and to characterise the sublines of S.
arXiv:1409.6794v1 fatcat:j5kz5cbsynadxo3iwzuiqz4dye