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

Abstract

In this paper we contribute towards the classification of partially symmetric tensors in F 3 q ⊗ S 2 F 3 q , q even, by classifying planes which intersect the Veronese surface V(F q ) in at least one point, under the action of K ≤ PGL(6, q), K ∼ = PGL(3, q), stabilising the Veronese surface. We also determine a complete set of geometric and combinatorial invariants for each of the orbits.