Mixed partitions of projective geometries (Q1580539)

A cap in a projective space is a set of points no three of which are collinear. The authors investigate mixed partitions of projective spaces, consisting of caps, all of which have the same geometric nature, and of up to two subspaces. Starting from a Singer cycle of \(PG(n-1,q)\), they construct a mixed partition of \(PG(2n-1,q)\) into two \((n-1)\)-subspaces and caps of size \((q^n -1)/(q-1)\) or \((q^n -1)/(q+1)\) if \(n\) is odd or even, respectively. Similar constructions are applied to obtain mixed partitions of quadrics and of Hermitian varieties.