Partitioning projective geometries into Segre varieties

Using suitable subgroups of Singer cyclic groups we prove some properties of regular spreads and Segre varieties, which in turn yield a necessary and sufficient condition for partitioning a finite projective space into such varieties.In ricordo di Giuseppe TalliniResearch performed within the activity of G.N.S.A.G.A. of C.N.R. with the support of the Italian Ministry for Research and Technology