Two projectively generated subsets of the Hermitian surface

Abstract

Using a variation of Seydewitz's method of projective generation of quadrics we define two algebraic surfaces of PG(3, q 2 ), called elliptic Q F -sets and semi-hyperbolic Q F -sets, and we show that these surfaces are contained in the Hermitian surface of PG(3, q 2 ). Also, we characterize a semi-hyperbolic Q F -set as the intersection of two Hermitian surfaces. Finally we describe all possible configurations of the absolute set of an α-correlation in PG(2, q 2 ), where α is the involutory automorphism of GF(q 2 ).