Hyperplanes of symplectic dual polar spaces: a survey (Q1700423)

Let \(W(2n-1,\mathbb{F})\) be the symplectic polar space. The dual symplectic polar space \(DW(2n-1,\mathbb{F})\) is the point-line geometry where the points are the generators of \(W(2n-1,\mathbb{F})\), the lines are the next-to-maximal subspaces of \(W(2n-1,\mathbb{F})\), and incidence is reverse containment. A set of points \(H\) of \(DW(2n-1,\mathbb{F})\) is called a \textit{hyperplane} if every line of \(DW(2n-1,\mathbb{F})\) meets \(H\) in one point or is completely contained in \(H\). The author presents in this article a survey on results about hyperplanes of \(DW(2n-1,\mathbb{F})\). This includes constructions of such hyperplanes, classification results and characterization results. He also considers the question which hyperplanes arise from full projective embeddings.