Hyperplane skew resolutions and their applications

Abstract A skew resolution in AG(n, q) is a partition of the lines of the geometry into classes (skew resolution classes) such that any two distinct lines in a class are disjoint and not parallel. In this paper we consider a special type of skew resolution. A hyperplane skew resolution R is a skew resolution having the property that for each class S of R there exists a unique parallel class P of hyperplanes in G such that each line of S traverses the members of P. In this paper we investigate the existence of hyperplane skew resolutions and their application to the line packing problem in PG(n, q) and other combinatorial designs.