A new combinatorial characterization of (quasi)-Hermitian surfaces.

In this paper, we present a combinatorial characterization of a quasi-Hermitian surface as a set H of points of PG (3 , q) , q = p 2 h h ≥ 1 , p a prime number and q ≠ 4 , having the same size as the Hermitian surface and containing no plane, such that either a line is contained in H or intersects H in at most q + 1 points and every plane intersects H in at least q q + 1 points. Moreover, if there is no external line, the set H is a Hermitian surface. [ABSTRACT FROM AUTHOR]