The m-covers and m-ovoids of generalised quadrangles and related structures

Melissa Chuekmun Lee

The m-covers and m-ovoids of generalised quadrangles and related structures

Melissa Chuekmun Lee

Research output: Thesis › Master's Thesis

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Abstract

Although many abstractions of hemisystems of H(3,q²) have been introduced since the first infinite family was discovered by Cossidente and Penttila in 2005, none have been applied to relative hemisystems . This is the main focus of this dissertation. We prove that every nontrivial relative m-cover is a relative hemisystem. We also give the first examples of relative hemisystems on nonclassical generalised quadrangles and study other generalisations in the classical case. Finally, we present computational results on the nonexistence of (q+1)12-ovoids of DH(5, q²) for q=3 and 5, using a simplification of the problem
to (q+1)/2-ovoids of DW(5, q).

Original language	English
Qualification	Masters
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Bamberg, John, Supervisor Giudici, Michael, Supervisor
Award date	8 Aug 2016
Publication status	Unpublished - 2016

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THESIS - MASTER OF PHILOSOPHY - LEE Melissa Chuekmun - 2016
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title = "The m-covers and m-ovoids of generalised quadrangles and related structures",

abstract = "Although many abstractions of hemisystems of H(3,q2) have been introduced since the first infinite family was discovered by Cossidente and Penttila in 2005, none have been applied to relative hemisystems . This is the main focus of this dissertation. We prove that every nontrivial relative m-cover is a relative hemisystem. We also give the first examples of relative hemisystems on nonclassical generalised quadrangles and study other generalisations in the classical case. Finally, we present computational results on the nonexistence of (q+1)12-ovoids of DH(5, q2) for q=3 and 5, using a simplification of the problemto (q+1)/2-ovoids of DW(5, q).",

keywords = "Association scheme, Generalised quadrangle, Relative hemisystem, Dual polar space",

author = "Lee, {Melissa Chuekmun}",

year = "2016",

language = "English",

school = "The University of Western Australia",

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TY - THES

T1 - The m-covers and m-ovoids of generalised quadrangles and related structures

AU - Lee, Melissa Chuekmun

PY - 2016

Y1 - 2016

N2 - Although many abstractions of hemisystems of H(3,q2) have been introduced since the first infinite family was discovered by Cossidente and Penttila in 2005, none have been applied to relative hemisystems . This is the main focus of this dissertation. We prove that every nontrivial relative m-cover is a relative hemisystem. We also give the first examples of relative hemisystems on nonclassical generalised quadrangles and study other generalisations in the classical case. Finally, we present computational results on the nonexistence of (q+1)12-ovoids of DH(5, q2) for q=3 and 5, using a simplification of the problemto (q+1)/2-ovoids of DW(5, q).

AB - Although many abstractions of hemisystems of H(3,q2) have been introduced since the first infinite family was discovered by Cossidente and Penttila in 2005, none have been applied to relative hemisystems . This is the main focus of this dissertation. We prove that every nontrivial relative m-cover is a relative hemisystem. We also give the first examples of relative hemisystems on nonclassical generalised quadrangles and study other generalisations in the classical case. Finally, we present computational results on the nonexistence of (q+1)12-ovoids of DH(5, q2) for q=3 and 5, using a simplification of the problemto (q+1)/2-ovoids of DW(5, q).

KW - Association scheme

KW - Generalised quadrangle

KW - Relative hemisystem

KW - Dual polar space

M3 - Master's Thesis

ER -

The m-covers and m-ovoids of generalised quadrangles and related structures

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