Subplane covered nets and semipartial geometries

Using the characterization theorems for (semi)partial geometries which satisfy the diagonal axiom, we prove that subplane covered nets or equivalently (n - 1)-regulus nets are isomorphic to the dual of the geometry H(q)n+1 with point set, the set of points of a projective space SIGMA congruent-to PG(n + 1, q) which do not belong to a fixed subspace H congruent-to PG(n - 1, q) and with line set, the set of lines of SIGMA-skew to H. Moreover we discuss some combinatorial problems on subplane covered nets. Some of the results are known in the literature and have group theoretic proofs, our proofs however are geometrical