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^2h h ≥ 1, p a prime number and q 6 different from 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.
A new combinatorial characterization of (quasi)– Hermitian surfaces
Vito Napolitano
2023
Abstract
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^2h h ≥ 1, p a prime number and q 6 different from 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.File in questo prodotto:
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