Maximal partial spreads of polar spaces (Q528987)

Summary: Some constructions of maximal partial spreads of finite classical polar spaces are provided. In particular we show that, for \(n \geq 1\), \(\mathcal{H}(4n-1,q^2)\) has a maximal partial spread of size \(q^{2n}+1\), \(\mathcal{H}(4n+1,q^2)\) has a maximal partial spread of size \(q^{2n+1}+1\) and, for \(n \geq 2\), \(\mathcal{Q}^+(4n-1,q)\), \(\mathcal{Q}(4n-2,q)\), \(\mathcal{W}(4n-1,q)\), \(q\) even, \(\mathcal{W}(4n-3,q)\), \(q\) even, have a maximal partial spread of size \(q^n+1\).