Some non-existence results on \(m\)-ovoids in classical polar spaces

In this paper we develop non-existence results for \(m\)-ovoids in the classical polar spaces \(Q^-(2r+1,q), W(2r-1,q)\) and \(H(2r,q^2)\) for \(r>2\). In [4] a lower bound on \(m\) for the existence of \(m\)-ovoids of \(H(4,q^2)\) is found by using the connection between \(m\)-ovoids, two-charac...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: De Beule, Jan, Mannaert, Jonathan, Valentino Smaldore
Format: Article
Language:English
Subjects:
Collinearity
Combinatorial analysis
Lower bounds
Online Access:Get full text
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Summary:In this paper we develop non-existence results for \(m\)-ovoids in the classical polar spaces \(Q^-(2r+1,q), W(2r-1,q)\) and \(H(2r,q^2)\) for \(r>2\). In [4] a lower bound on \(m\) for the existence of \(m\)-ovoids of \(H(4,q^2)\) is found by using the connection between \(m\)-ovoids, two-character sets, and strongly regular graphs. This approach is generalized in [3] for the polar spaces \(Q^-(2r+1,q), W(2r-1,q)\) and \(H(2r,q^2)\), \(r>2\). In [1] an improvement for the particular case \(H(4,q^2)\) is obtained by exploiting the algebraic structure of the collinearity graph, and using the characterization of an \(m\)-ovoid as an intruiging set. In this paper, we use an approach based on geometrical and combinatorial arguments, inspired by the results from [10], to improve the bounds from [3].
ISSN:2331-8422