On Some \(2\)-Tight Sets of Polar Spaces

Abstract

Let \(\Pi\) be a finite polar space of rank \(n \geq 2\) fully embedded into a projective space \(\Sigma\). In this note, we determine all tight sets of \(\Pi\) of the form \((\Sigma_1 \cap \mathcal{P}) \cup (\Sigma_2 \cap \mathcal{P})\), where \(\mathcal{P}\) denotes the point set of \(\Pi\) and \(\Sigma_1, \Sigma_2\) are two mutually disjoint subspaces of \(\Sigma\). In this way, we find two families of \(2\)-tight sets of elliptic polar spaces that were not described before in the literature.