Hyperovals of $H(3,q^2)$ when $q$ is even

Name: Hyperovals of $H(3,q^2)$ when $q$ is even
Keywords: Hermitian surface; Hyperoval; Symplectic subquadrangle; Theoretical Computer Science; Discrete Mathematics and Combinatorics; Computational Theory and Mathematics, Symplectic subquadrangle, Hermitian surface; Hyperoval; Symplectic subquadrangle;polar spaces;m-ovoids, Blocking sets, ovals, $k$-arcs, hyperoval, Hermitian surface, Theoretical Computer Science, symplectic subquadrangle, Computational Theory and Mathematics, FOS: Mathematics

Antonio Cossidente; Oliver H. King; Giuseppe Marino 0002

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Hyperovals of $H(3,q^2)$ when $q$ is even

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2012Embargo end date: 01 Jan 2012 Italy, United Kingdom Publisher:arXivJournal:J. Comb. Theory A, volume 120, pages 1,131-1,140

Authors: Antonio Cossidente; Oliver H. King; Giuseppe Marino 0002;

doi: 10.48550/arxiv.1211.3649

arXiv: 1211.3649

handle: 11588/739042 , 11591/184092 , 11563/49634

Hyperovals of $H(3,q^2)$ when $q$ is even

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Abstract

For even $q$, a group $G$ isomorphic to $PSL(2,q)$ stabilizes a Baer conic inside a symplectic subquadrangle ${\cal W}(3,q)$ of ${\cal H}(3,q^2)$. In this paper the action of $G$ on points and lines of ${\cal H}(3,q^2)$ is investigated. A construction is given of an infinite family of hyperovals of size $2(q^3-q)$ of ${\cal H}(3,q^2)$, with each hyperoval having the property that its automorphism group contains $G$. Finally it is shown that the hyperovals constructed are not isomorphic to known hyperovals.

Submitted

Countries

Italy, United Kingdom

Related Organizations

University of Campania "Luigi Vanvitelli"
Italy
University Federico II of Naples
Italy
Newcastle University
United Kingdom
University of Basilicata
Italy

Keywords

Hermitian surface; Hyperoval; Symplectic subquadrangle; Theoretical Computer Science; Discrete Mathematics and Combinatorics; Computational Theory and Mathematics, Symplectic subquadrangle, Hermitian surface; Hyperoval; Symplectic subquadrangle;polar spaces;m-ovoids, Blocking sets, ovals, $k$-arcs, hyperoval, Hermitian surface, Theoretical Computer Science, symplectic subquadrangle, Computational Theory and Mathematics, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Hyperoval

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