The tangent splash in \PG(6,q)

2013/05/29 by S. G. Barwick, Wen-Ai Jackson, Barwick, S. G. +2 · 1 citation
Mathematics · #51E20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #math.CO #msc:51E20

paper · pdf · doi:10.48550/arxiv.1305.6674

arXiv admin note: substantial text overlap with arXiv:1303.5509

arxiv created 2013/05/29 · openalex publication_date 2013/05/29 · arxiv updated 2013/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let B be a subplane of PG(2,q³) of order q that is tangent to ℓ_∞. Then the tangent splash of B is defined to be the set of q²+1 points of ℓ_∞ that lie on a line of B. In the Bruck-Bose representation of PG(2,q³) in PG(6,q), we investigate the interaction between the ruled surface corresponding to B and the planes corresponding to the tangent splash of B. We then give a geometric construction of the unique order-q-subplane determined by a given tangent splash and a fixed order-q-subline.

Citations

• An investigation of the tangent splash of a subplane of PG(2,q³)

Cited by

• The exterior splash in PG(6,q): Transversals

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• An investigation of the tangent splash of a subplane of PG(2,q³)
• The exterior splash in PG(6,q): Special conics
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• A Characterisation of Tangent Subplanes of PG(2,q³)
• Exterior splashes and linear sets of rank 3