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

Nour Alnajjarine; Michel Lavrauw

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

Combinatorics 2022-09-20 v1 Algebraic Geometry

Authors: Nour Alnajjarine , Michel Lavrauw

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.

Keywords

veronese surface finite fields partially symmetric tensors plane classification geometric invariants combinatorial invariants

Cite

@article{arxiv.2209.08354,
  title  = {A classification of planes intersecting the Veronese surface over finite fields of even order},
  author = {Nour Alnajjarine and Michel Lavrauw},
  journal= {arXiv preprint arXiv:2209.08354},
  year   = {2022}
}

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

Abstract

Keywords

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