Some subsets of the Hermitian curve
type: Item
instance of: scholarly article
title: Some subsets of the Hermitian curve
zbMATH Open document ID: 1024.51011
DOI: 10.1016/S0195-6698(02)00143-9
author: Nicola Durante
author: Giorgio Donati
published in: European Journal of Combinatorics
publication date: 2003-04-02T00:00:00Z
review text: 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 \(PG(4,q)\).
Mathematics Subject Classification ID: 51E30
zbMATH DE Number: 1891299
reviewed by: Antonio Cossidente
MaRDI profile type: Publication
cites work: Q3227204
cites work: A characterization of the classical unital
cites work: Ovoids of PG(3,q ), q Even, with a Conic Section
cites work: The construction of translation planes from projective spaces
cites work: Linear representations of projective planes in projective spaces
cites work: Concerning a characterisation of Buekenhout-Metz unitals
cites work: (q2+q+l)-Sets of Type (0,1,2,q+l) in Translation Planes of Order q2
cites work: Elementi di geometria non lineare sopra un corpo sghembo
cites work: Q3902097
description: scientific article; zbMATH DE number 1891299