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arXiv · 2305.03346

Classification of spreads of Tits quadrangles of order 64

Giusy Monzillo·Tim Penttila·Alessandro Siciliano
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Abstract

Brown et al. provide a representation of a spread of the Tits quadrangle $T_2(\mathcal O)$, $\mathcal O$ an oval of $\mathrm PG(2,q)$, $q$ even, in terms of a certain family of $q$ ovals of $\mathrm PG(2,q)$. By combining this representation with the Vandendriessche classification of hyperovals in $\mathrm PG(2,64)$ and the classification of flocks of the quadratic cone in $\mathrm PG(3,64)$, recently given by the authors, in this paper, we classify all the spreads of $T_2(\mathcal O)$, $\mathcal O$ an oval of $\mathrm PG(2,64)$, up to equivalence. These complete the classification of spreads of $T_2(\mathcal O)$ for $q\le 64$.

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Giusy Monzillo, Tim Penttila, Alessandro Siciliano. 2023-05-05. Classification of spreads of Tits quadrangles of order 64. https://arxiv.org/abs/2305.03346

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