Affine Geometries Obtained from Projective Planes and Skew Resolutions on AG(3,q)

Publisher Summary This chapter presents a construction of AG(n+l,q) from the projective plane PG(2,qn). This construction can be applied to construct the skew resolutions of the lines in AG(n,q) and pairs of orthogonal resolutions. It is shown that there exists a skew resolution of the lines in AG(3,q) by constructing a resolution of the lines in PG(3,q). A skew resolution in AG(n,q) along with the natural resolution of lines in AG(n,q) obtained from parallelism form a pair of orthogonal resolutions. The finite affine geometry AG(n,q) is usually obtained from a vector space over a Galois field. A finite affine plane is more simply defined to be a (q2,q,l)-BIBD. It is well known that an affine plane has a unique resolution (parallelism).