Nicola Durante

Some subsets of the Hermitian curve

Three types of subsets of PG(2, q2) of type (0, 1, 2, q + 1) are defined, namely CF-sets, K-sets and H-sets. These subsets may also be obtained as the intersection of the Hermitian curve H with Baer subpencils of lines with vertex not on H. It is shown that under the Bruck-Bose representation these subsets correspond to three-dimensional elliptic quadrics, quadratic cones and hyperbolic quadrics, respectively contained in suitable hyperplanes of PG(4, q).

A hemisystem of a nonclassical generalised quadrangle

The concept of a hemisystem of a generalised quadrangle has its roots in the work of B. Segre, and this term is used here to denote a set of points

On the intersection of a Hermitian curve with a conic

{\mathcal{H}}

On the intersection of two subgeometries of PG(n, q)

such that every line ℓ meets

The geometry of some two-character sets

{\mathcal{H}}

Symmetries of BLT-Sets

in half of the points of ℓ. If one takes the point-line geometry on the points of the hemisystem, then one obtains a partial quadrangle and hence a strongly regular point graph. The only previously known hemisystems of generalised quadrangles of order (q, q2) were those of the elliptic quadric