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arXiv · 2506.23330

Characterization of non-singular hyperplanes of $H\left(s,q^2\right)$ in $\mathrm{P G}\left(s, q^2\right)$

Stuti Mohanty·Bikramaditya Sahu
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Abstract

In this paper, we present a combinatorial characterization of the hyperplanes associated with non-singular hermitian varieties ${H}\left(s, q^2\right)$ in the projective space $\mathrm{PG}\left(s,q^2\right)$ where $s\geq3$ and $q>2$. By analyzing the intersection numbers of hyperplanes with points and co-dimension $2$ subspaces, we establish necessary and sufficient conditions for a hyperplane to be part of the hermitian variety. This approach extends previous characterizations of hermitian varieties based on intersection properties, providing a purely combinatorial method for identifying their hyperplanes.

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Stuti Mohanty, Bikramaditya Sahu. 2025-06-29. Characterization of non-singular hyperplanes of $H\left(s,q^2\right)$ in $\mathrm{P G}\left(s, q^2\right)$. https://arxiv.org/abs/2506.23330

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