Classification Results for Hyperovals of Generalized Quadrangles

DOI10.1007/978-3-030-52200-1_15zbMath1503.51001OpenAlexW3041881918MaRDI QIDQ5039567

Bart De Bruyn

Publication date: 13 October 2022

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-52200-1_15

zbMATH Keywords

idealgeneralized quadranglehyperovaleven setpseudo-embedding

Mathematics Subject Classification ID

Generalized quadrangles and generalized polygons in finite geometry (51E12) Combinatorial aspects of finite geometries (05B25) Computational methods for problems pertaining to geometry (51-08)

Uses Software

• GAP
• SageMath

Cites Work

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• Hyperovals of \(H(3,q^2)\) when \(q\) is even
• Hyperovals on \(\mathcal{H}(3,q^2)\) left invariant by a group of order \(6(q+1)^3\)
• Hyperovals of Hermitian polar spaces
• The pseudo-hyperplanes and homogeneous pseudo-embeddings of \(\mathrm{AG}(n, 4)\) and \(\mathrm{PG}(n, 4)\)
• Extended generalized quadrangles
• Finite generalized quadrangles
• A computer search for finite projective planes of order 9
• Locally polar spaces and related rank 3 groups
• Hyperovals arising from a Singer group action on \(\mathcal{H}(3, q^2)\), \(q\) even
• On the foundations of polar geometry
• The triangular extensions of a generalized quadrangle of order \((3,3)\)
• The pseudo-hyperplanes and homogeneous pseudo-embeddings of the generalized quadrangles of order \((3,t)\)
• The homogeneous pseudo-embeddings and hyperovals of the generalized quadrangle \(H(3,4)\)
• Hyperovals on \(\mathcal H(3,q^2)\)
• Hyperoval constructions on the Hermitian surface
• New infinite families of hyperovals on \(\mathcal H(3,q^2)\), \(q\) odd
• The extensions of the generalized quadrangle of order (3,9)
• The Non-Existence of Finite Projective Planes of Order 10
• Uniqueness of the Projective Plane of Order Eight
• General Galois Geometries
• Extensions of GQ(4,2), the description of hyperovals
• Pseudo-embeddings and pseudo-hyperplanes
• The nonexistence of ovals in a projective plane of order 10

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