Recognizing sets of generators in finite polar spaces (Q2305995)

Let \(\mathcal P\) be a non-degenerate finite embedded polar space of rank \(n \geq 2\) admitting a hyperplane section which is a polar space of the same rank. The authors present a combinatorial characterization of the set \(\mathcal S\) of generators of the embedded polar space. The characterization is given in terms of the number of generators in \(\mathcal S\) which intersect a given generator of \(\mathcal P\) in in a subspace of rank \(n-2\). This number should depend only on whether the given generator is in \(\mathcal S\) or not. The result is an improvement of the main result of \textit{J. De Beule} and \textit{M. De Boeck} [Discrete Math. 341, No. 10, 2841--2845 (2018; Zbl 1393.05066)].