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arXiv · 2209.08354

A classification of planes intersecting the Veronese surface over finite fields of even order

Nour Alnajjarine·Michel Lavrauw
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Abstract

In this paper we contribute towards the classification of partially symmetric tensors in $\mathbb{F}_q^3\otimes S^2\mathbb{F}_q^3$, $q$ even, by classifying planes which intersect the Veronese surface $\mathcal{V}(\mathbb{F}_q)$ in at least one point, under the action of $K\leq \rm{PGL}(6,q)$, $K\cong \rm{PGL}(3,q)$, stabilising the Veronese surface. We also determine a complete set of geometric and combinatorial invariants for each of the orbits.

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Nour Alnajjarine, Michel Lavrauw. 2022-09-17. A classification of planes intersecting the Veronese surface over finite fields of even order. https://arxiv.org/abs/2209.08354

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