On linear partial spreads

A linear partial spread is a set of mutually skew lines of some P(V ) – where V is a finite dimensional vector space over a field – that are characterized by the property that their images under the Plücker embedding are in a given subspace of P (∧2 V ); it is a linear spread if the lines in it cover the whole space. We will provide methods to construct linear partial spreads, and characterize some of the linear partial spreads built in this way by means of the concept of transversal line.