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

2022/09/17 by Nour Alnajjarine, Alnajjarine, Nour, Michel Lavrauw +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Tensor decomposition and applications

paper · doi:10.48550/arxiv.2209.08354

openalex publication_date 2022/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we contribute towards the classification of partially symmetric tensors in \mathbbF_q³⊗ S²\mathbbF_q³, q even, by classifying planes which intersect the Veronese surface V(\mathbbF_q) in at least one point, under the action of K≤ \rmPGL(6,q), K≅ \rmPGL(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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