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Mathematics
Volume 13
Issue 9
10.3390/math13091489
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Review

Arcs, Caps and Generalisations in a Finite Projective Space

by
James W. P. Hirschfeld
1 and
Joseph A. Thas
2,*
1
Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK
2
Department of Mathematics, Ghent University, 9000 Gent, Belgium
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(9), 1489; https://doi.org/10.3390/math13091489
Submission received: 18 March 2025 / Revised: 23 April 2025 / Accepted: 25 April 2025 / Published: 30 April 2025
(This article belongs to the Section B: Geometry and Topology)
Versions Notes

Abstract

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.
Keywords: arc; cap; generalised oval; generalised ovoid; translation; finite projective space arc; cap; generalised oval; generalised ovoid; translation; finite projective space

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MDPI and ACS Style

Hirschfeld, J.W.P.; Thas, J.A. Arcs, Caps and Generalisations in a Finite Projective Space. Mathematics 2025, 13, 1489. https://doi.org/10.3390/math13091489

AMA Style

Hirschfeld JWP, Thas JA. Arcs, Caps and Generalisations in a Finite Projective Space. Mathematics. 2025; 13(9):1489. https://doi.org/10.3390/math13091489

Chicago/Turabian Style

Hirschfeld, James W. P., and Joseph A. Thas. 2025. "Arcs, Caps and Generalisations in a Finite Projective Space" Mathematics 13, no. 9: 1489. https://doi.org/10.3390/math13091489

APA Style

Hirschfeld, J. W. P., & Thas, J. A. (2025). Arcs, Caps and Generalisations in a Finite Projective Space. Mathematics, 13(9), 1489. https://doi.org/10.3390/math13091489

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