Characterising elliptic and hyperbolic hyperplanes of the parabolic quadric \Q(2n,q)

Geertrui Van de Voorde; Jeroen Schillewaert

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arxiv 2111.09443 v1 pith:FIR33KR6 submitted 2021-11-17 math.CO

Characterising elliptic and hyperbolic hyperplanes of the parabolic quadric Q(2n,q)

Jeroen Schillewaert , Geertrui Van de Voorde This is my paper

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We provide a natural characterisation for the sets of elliptic and hyperbolic hyperplanes of the parabolic quadric Q(2n,q) when q is even. This characterisation is based on the number of elements of these sets through points and codimension 2 spaces and generalises [S. Barwick, A. Hui, and W-A. Jackson. Characterising elliptic solids of Q(4,q), q even. Discrete Math., 343 (6) (2020), 111857] and [S. Barwick, A. Hui, W-A. Jackson, and J. Schillewaert. Characterising hyperbolic solids of Q(4,q), q even. Des. Codes Cryptogr., 88 (1) (2020), 33--39.].

Characterising elliptic and hyperbolic hyperplanes of the parabolic quadric Q(2n,q)

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