About: Spread (projective geometry)

A frequently studied problem in discrete geometry is to identify ways in which an object can be covered by other simpler objects such as points, lines, and planes. In projective geometry, a specific instance of this problem that has numerous applications is determining whether, and how, a projective space can be covered by pairwise disjoint subspaces which have the same dimension; such a partition is called a spread. Specifically, a spread of a projective space , where is an integer and a division ring, is a set of -dimensional subspaces, for some such that every point of the space lies in exactly one of the elements of the spread.