On two new classes of semibiplanes Original Research Article

Two new infinite classes of semibiplanes are defined by considering for any q = 2h, h > 1, a point-plane pair (p, π) in PG(3, q), a hyperoval O in the star of p and a dual hyperoval O∗ in the plane π in suitable mutual position. These geometries are called of flag type or anti-flag type according to p and π are incident or not. By deleting some suitable elements from the semibiplanes of flag type we obtain another family of semibiplanes. In all of cases some quotients are defined. For q = 4, the semibiplane of anti-flag type is a flag-transitive geometry already given by Pasini and Yoshiara.