Points and hyperplanes of the universal embedding space of the dual polar space DW\((5,q)\), \(q\) odd (Q1024875)

The paper under review is a contribution to the task of classifying all hyperplanes of finite dual polar spaces of small rank. The authors determine all geometric hyperplanes of the dual polar space DW\((5,q)\) for odd \(q\) that arise from a certain embedding. For even \(q\) this was done by Pralle (\(q=2\)) [\textit{H. Pralle}, Exp. Math. 14, No.~3, 373--384 (2005; Zbl 1093.51012)], and by the second author [Discrete Math. 309, No.~2, 304--321 (2009; Zbl 1160.51006)]. The approach is based on examining the orbits of the automorphism group of DW\((5,q)\).