Ovoidal maximal subspaces of polar spaces
- Author
- Antonio Pasini and Hendrik Van Maldeghem (UGent)
- Organization
- Abstract
- Let S be a polar space of rank n ≥ 2. A set of mutually non-collinear points of S is trivially a subspace of S . We call it an ovoidal subspace. It is well known that when n = 2 all ovoids are maximal subspaces. However, as we shall see in this paper, when n > 2 ovoids exist which are not maximal subspaces. Moreover, in the finite case, not all polar spaces admit ovoids. So, it is natural to ask whether ovoidal maximal subspaces exist in any polar space. In this paper we provide a basically affirmative answer to this question, proving that ovoidal maximal subspaces exist in all polar spaces but the following ones: Q2n(2) with n even and greater than 2, Q+ 2n−1(2) with n ≡ 2; 3 (mod 4) and greater than 2 and Q− 2n+1(2) with n ≡ 0; 3 (mod 4).
- Keywords
- Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01HWDCSDDCDKZY2T7NR6686WR9
- MLA
- Pasini, Antonio, and Hendrik Van Maldeghem. “Ovoidal Maximal Subspaces of Polar Spaces.” Algebraic Combinatorics and the Monster Group, edited by Alexander A. Ivanov, 1st ed., vol. 487, Cambridge University, 2023, pp. 369–402, doi:10.1017/9781009338073.009.
- APA
- Pasini, A., & Van Maldeghem, H. (2023). Ovoidal maximal subspaces of polar spaces. In A. A. Ivanov (Ed.), Algebraic combinatorics and the monster group (1st ed., Vol. 487, pp. 369–402). https://doi.org/10.1017/9781009338073.009
- Chicago author-date
- Pasini, Antonio, and Hendrik Van Maldeghem. 2023. “Ovoidal Maximal Subspaces of Polar Spaces.” In Algebraic Combinatorics and the Monster Group, edited by Alexander A. Ivanov, 1st ed., 487:369–402. Cambridge, UK: Cambridge University. https://doi.org/10.1017/9781009338073.009.
- Chicago author-date (all authors)
- Pasini, Antonio, and Hendrik Van Maldeghem. 2023. “Ovoidal Maximal Subspaces of Polar Spaces.” In Algebraic Combinatorics and the Monster Group, ed by. Alexander A. Ivanov, 487:369–402. 1st ed. Cambridge, UK: Cambridge University. doi:10.1017/9781009338073.009.
- Vancouver
- 1.Pasini A, Van Maldeghem H. Ovoidal maximal subspaces of polar spaces. In: Ivanov AA, editor. Algebraic combinatorics and the monster group. 1st ed. Cambridge, UK: Cambridge University; 2023. p. 369–402.
- IEEE
- [1]A. Pasini and H. Van Maldeghem, “Ovoidal maximal subspaces of polar spaces,” in Algebraic combinatorics and the monster group, 1st ed., vol. 487, A. A. Ivanov, Ed. Cambridge, UK: Cambridge University, 2023, pp. 369–402.
@incollection{01HWDCSDDCDKZY2T7NR6686WR9,
abstract = {{Let S be a polar space of rank n ≥ 2. A set of mutually non-collinear points of S is
trivially a subspace of S . We call it an ovoidal subspace. It is well known that when n = 2
all ovoids are maximal subspaces. However, as we shall see in this paper, when n > 2 ovoids
exist which are not maximal subspaces. Moreover, in the finite case, not all polar spaces
admit ovoids. So, it is natural to ask whether ovoidal maximal subspaces exist in any polar
space. In this paper we provide a basically affirmative answer to this question, proving that
ovoidal maximal subspaces exist in all polar spaces but the following ones: Q2n(2) with n
even and greater than 2, Q+ 2n−1(2) with n ≡ 2; 3 (mod 4) and greater than 2 and Q− 2n+1(2)
with n ≡ 0; 3 (mod 4).}},
author = {{Pasini, Antonio and Van Maldeghem, Hendrik}},
booktitle = {{Algebraic combinatorics and the monster group}},
editor = {{Ivanov, Alexander A.}},
isbn = {{9781009338042}},
issn = {{2634-3681}},
keywords = {{Mathematics (general),Mathematics,Discrete Mathematics Information Theory and Coding,Algebra}},
language = {{eng}},
pages = {{369--402}},
publisher = {{Cambridge University}},
series = {{London mathematical society lecture note series}},
title = {{Ovoidal maximal subspaces of polar spaces}},
url = {{http://doi.org/10.1017/9781009338073.009}},
volume = {{487}},
year = {{2023}},
}
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