Showing papers by "J. W. P. Hirschfeld published in 2016"
01 Jan 2016
TL;DR: In this paper, the authors define Hermitian varieties, Grassmann varieties, Veronese and Segre varieties, and embedded geometries for finite projective spaces of three dimensions.
Abstract: Terminology Quadrics Hermitian varieties Grassmann varieties Veronese and Segre varieties Embedded geometries Arcs and caps Appendix VI. Ovoids and spreads of finite classical polar spaces Appendix VII. Errata for Finite projective spaces of three dimensions and Projective geometries over finite fields Bibliography Index of notation Author index General index.
647 citations
01 Jan 2016
TL;DR: In this article, the main results on these topics are given, all without proof, all with the BLT-property, and all without proving the properties of sets with BLT property.
Abstract: In this chapter, ovoids, spreads and m-systems of finite classical polar spaces are introduced Also SPG-reguli, SPG-systems, BLT-sets and sets with the BLT-property are defined The main results on these topics are given, all without proof
28 citations
TL;DR: In this article, a lower bound for the size of complete (k, n)-arcs is established and shown to be a generalisation of a classical result by Barlotti.
Abstract: This paper examines subsets with at most n points on a line in the projective plane π q = PG(2, q) A lower bound for the size of complete (k, n)-arcs is established and shown to be a generalisation of a classical result by Barlotti A sufficient condition ensuring that the trisecants to a complete (k, 3)-arc form a blocking set B in the dual plane π∗ q is provided Finally, combinatorial arguments are used to show that, for q ≥ 17, plane (k, 3)-arcs satisfying a prescribed incidence condition do not attain the best known upper bound
16 citations