This paper establishes a beautiful relation between geometric \(t\)-spreads and group divisible designs the dual of which is again a group divisible design. Let \({\mathcal S}\) be a \(t\)-spread of \(PG(d,q)\), i.e. a partition of the point set of \(PG(d,q)\) in \(t\)-dimensional subspaces, called the component of \({\mathcal S}\). The authors construct a 1-design \({\mathcal G}({\mathcal S})\) from \({\mathcal S}\) as follows: the points of \({\mathcal G}({\mathcal S})\) are the points of \(PG(d,q)\) and the blocks of \({\mathcal G}({\mathcal S})\) are the hyperplanes \(H\) where all components of \({\mathcal S}\) contained in \(H\) are removed. Then they show that two points in the same component of \({\mathcal S}\) are incident with a constant number \(\lambda_ 1\) of blocks, and two points in different components are incident with a constant number \(\lambda_ 2\neq\lambda_ 1\) of blocks, hence \({\mathcal G}({\mathcal S})\) is a group divisible design. The main result of the paper under review is that the dual of \({\mathcal G}({\mathcal S})\) is also a group divisible design if and only if the \(t\)-spread \({\mathcal S}\) is regular, i.e. every \((2t+1)\)- dimensional subspace of \(PG(d,q)\) spanned by two components of \({\mathcal S}\) is covered by the components contained in it.