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Jan De Beule
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Klaus Metsch
Keywords:
Polar space, Tight set
Abstract
We show that an $x$-tight set of the Hermitian polar spaces $\mathrm{H}(4,q^2)$ and $\mathrm{H}(6,q^2)$ respectively, is the union of $x$ disjoint generators of the polar space provided that $x$ is small compared to $q$. For $\mathrm{H}(4,q^2)$ we need the bound $x<q+1$ and we can show that this bound is sharp.