The exterior splash in PG(6,q): Special conics [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_∞. 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 of PG(5,q). In this article we use the Bruck-Bose representation in PG(6,q) to give a geometric characterisation of special conics of π in terms of the covers of the exterior splash of π. We also
more » ... estigate properties of order-q-subplanes with a common exterior splash, and study the intersection of two exterior splashes.
arXiv:1410.4269v1 fatcat:exrug5lff5hptna72c4aeaww6e