Some subsets of the Hermitian curve
The authors define three types of subsets of \(PG(2,q^2)\) of type \((0,1,2,q+1)\) with respect to lines and call them \(C_F\)-sets, \(K\)-sets and \(H\)-sets. Such subsets are also obtainable intersecting an Hermitian curve of \(PG(2,q^2)\) with suitable Baer subpencils of lines. Using the Bruck-Bose representation, the authors prove that their subsets correspond to three-dimensional elliptic quadrics, quadratic cones and hyperbolic quadrics inside certain hyperplanes of \(PG(4,q)\).
scientific article; zbMATH DE number 1891299