ABSTRACT
In this chapter, we consider (partial) spreads in terms of projective spaces. This has the obvious advantage of enabling results in projective geometry to be directly applied to the study of spreads and translation planes. We begin by restating the Andre notion of a spread in terms of projective spaces:
Definition 15.1.1 Let Σ := PG(V,K) denote the projective space associ ated with a vector space over a skewfield if. If C is a projective subspace, denote by [C] the associated vector space. Then a ‘partial spread’ in Σ is any collection S of pairwise skew subspaces of Σ, such that if A, B £ Σ are distinct and u £ [A] U [B] is any projective point, then there is a line ί through u that meets A and B. (Equivalently, V = [A] 0 [B].) The partial spread S is a spread if every projective point of Σ lies in a some component ofS.
