A Characterisation of Tangent Subplanes of PG(2,q³)

2012/04/23 by S. G. Barwick, Wen-Ai Jackson, Barwick, S. G. +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1204.4953

arxiv created 2012/04/23 · arxiv updated 2012/04/24

Abstract

In: S.G. Barwick and W.A. Jackson. Sublines and subplanes of PG(2,q³) in the Bruck--Bose representation in PG(6,q). Finite Fields Th. App. 18 (2012) 93--107., the authors determine the representation of order-q-subplanes and order-q-sublines of PG(2,q³) in the Bruck-Bose representation in PG(6,q). In particular, they showed that an order-q-subplane of PG(2,q³) corresponds to a certain ruled surface in PG(6,q). In this article we show that the converse holds, namely that any ruled surface satisfying the required properties corresponds to a tangent order-q-subplane of PG(2,q³).

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