The characterization of cones as pointsets with 3 intersection numbers

TL;DR

This paper generalizes the combinatorial characterization of cones in projective spaces, extending previous results to higher dimensions and including hyperoval and maximal arc cones, enhancing understanding of their geometric and combinatorial properties.

Contribution

It extends the characterization of cones from PG(3,q) to arbitrary dimensions and incorporates hyperoval and maximal arc cones, broadening the scope of geometric combinatorics.

Findings

Generalization of cone characterization to higher dimensions

Extension to hyperoval and maximal arc cones

Enhanced understanding of intersection properties

Abstract

Innamorati and Zuanni have provided a combinatorial characterization of Baer and unital cones in PG(3,q). The current paper generalizes these results to arbitrary dimension. Furthermore, these results are extended to hyperoval and maximal arc cones.