Hermitian Varieties in a Finite Projective Space PG(N, q2)

Abstract

The geometry of quadric varieties (hypersurfaces) in finite projective spaces of N dimensions has been studied by Primrose (12) and Ray-Chaudhuri (13). In this paper we study the geometry of another class of varieties, which we call Hermitian varieties and which have many properties analogous to quadrics. Hermitian varieties are defined only for finite projective spaces for which the ground (Galois field) GF(q2) has order q2, where q is the power of a prime. If h is any element of GF(q2), then = hq is defined to be conjugate to h.