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

The article delves into the classification of planes intersecting the Veronese surface over finite fields of even order, focusing on the action of the group that leaves the Veronese surface invariant. It discusses the classification of partially symmetric tensors and their orbits, highlighting the geometric approach used in previous works by the authors. The classification is based on the point-orbit distributions and line-orbit distributions of the planes, with a particular focus on planes meeting the Veronese surface in at least one point. The paper also includes a comparison with the classification over finite fields of odd order, emphasizing the fundamental differences in the geometry of the Veronese surface in even characteristic. Additionally, the article provides a historical context and discusses the implications of the classification for the study of linear systems of conics.