Arcs, Caps and Generalisations in a Finite Projective Space

Arcs and caps are fundamental structures in finite projective spaces. They can be generalised. Here, a survey is given of some important results on these objects, in particular on generalised ovals and generalised ovoids. This paper also contains recent results and several open problems.

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Main Authors: James W. P. Hirschfeld, Joseph A. Thas
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/13/9/1489
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author James W. P. Hirschfeld
Joseph A. Thas
author_facet James W. P. Hirschfeld
Joseph A. Thas
author_sort James W. P. Hirschfeld
collection DOAJ
description Arcs and caps are fundamental structures in finite projective spaces. They can be generalised. Here, a survey is given of some important results on these objects, in particular on generalised ovals and generalised ovoids. This paper also contains recent results and several open problems.
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issn 2227-7390
language English
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spelling doaj-art-cfe54815b22b46e29cc8c862ce20089b2025-08-20T01:49:28ZengMDPI AGMathematics2227-73902025-04-01139148910.3390/math13091489Arcs, Caps and Generalisations in a Finite Projective SpaceJames W. P. Hirschfeld0Joseph A. Thas1Department of Mathematics, University of Sussex, Brighton BN1 9QH, UKDepartment of Mathematics, Ghent University, 9000 Gent, BelgiumArcs and caps are fundamental structures in finite projective spaces. They can be generalised. Here, a survey is given of some important results on these objects, in particular on generalised ovals and generalised ovoids. This paper also contains recent results and several open problems.https://www.mdpi.com/2227-7390/13/9/1489arccapgeneralised ovalgeneralised ovoidtranslationfinite projective space
spellingShingle James W. P. Hirschfeld
Joseph A. Thas
Arcs, Caps and Generalisations in a Finite Projective Space
Mathematics
arc
cap
generalised oval
generalised ovoid
translation
finite projective space
title Arcs, Caps and Generalisations in a Finite Projective Space
title_full Arcs, Caps and Generalisations in a Finite Projective Space
title_fullStr Arcs, Caps and Generalisations in a Finite Projective Space
title_full_unstemmed Arcs, Caps and Generalisations in a Finite Projective Space
title_short Arcs, Caps and Generalisations in a Finite Projective Space
title_sort arcs caps and generalisations in a finite projective space
topic arc
cap
generalised oval
generalised ovoid
translation
finite projective space
url https://www.mdpi.com/2227-7390/13/9/1489
work_keys_str_mv AT jameswphirschfeld arcscapsandgeneralisationsinafiniteprojectivespace
AT josephathas arcscapsandgeneralisationsinafiniteprojectivespace