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arXiv · 2607.08135

Every special set of the Hermitian surface $\mathsf{H}(3,q^2)$ is classical

John Bamberg·Ethan Kealley
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Abstract

Special sets of the Hermitian surface $\mathsf{H}(3,q^2)$, $q$ odd, were introduced by Shult and Thas (1995) in order to construct new finite generalised quadrangles, yet only one example is known to exist and it gives rise to a classical generalised quadrangle. We show that there can be no other special sets of the Hermitian surface.

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John Bamberg, Ethan Kealley. 2026-07-10. Every special set of the Hermitian surface $\mathsf{H}(3,q^2)$ is classical. https://arxiv.org/abs/2607.08135

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