Vol. 11, No. 1, 2010

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Two projectively generated subsets of the Hermitian surface

Giorgio Donati and Nicola Durante

Vol. 11 (2010), No. 1, 99–114

Using a variation of Seydewitz’s method of projective generation of quadrics we define two algebraic surfaces of PG(3,q2), called elliptic QF-sets and semi-hyperbolic QF-sets, and we show that these surfaces are contained in the Hermitian surface of PG(3,q2). Also, we characterize a semi-hyperbolic QF-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,q2), where α is the involutory automorphism of GF(q2).

Hermitian surfaces, collineations, correlations
Mathematical Subject Classification 2010
Primary: 05B25, 51E20
Received: 17 March 2008
Accepted: 7 December 2008
Giorgio Donati
Nicola Durante