Bose-Burton type theorems for finite Grassmannians

In this paper we investigate both blocking sets with respect to the s-subspaces and covers with t-subspaces in a finite Grassmannian. We are especially interested in geometric descriptions of blocking sets and covers of minimum size. When such a description exists, we say it is a Bose-Burton type theorem. The canonical example of a blocking set with respect to the s-subspaces is the intersection of s linear complexes. In some cases such intersection is a blocking set of minimum size, that can occasionally be characterized by a Bose-Burton type theorem. In particular, this happens for the 1-blocking sets of the Grassmannian of planes of PG(5, q).