A combinatorial characterization of geometric spreads (Q1183967)

Autor's abstract: A \(t\)-spread in a projective space \(P=PG(d,q)\) is a set of \(t\)-dimensional subspaces which partitions the point set of \(P\). A \(t\)-spread \(S\) is called geometric if it induces a spread in any \((2t+1)\)-dimensional subspace containing at least two elements of \(S\). We characterize the geometric \(t\)-spreads \(S\) among all partial spreads in the first nontrivial case \(PG(3t+2,q)\) by the property that any subspace of dimension \(3t\) contains at least one element of \(S\). This is the first instance of a combinatorial characterization of geometric spreads.