English

A ruled quintic surface in $PG(6,q)$

Combinatorics 2019-06-12 v1

Abstract

In this article we look at a scroll of PG(6,q)PG(6,q) that uses a projectivity to rule a conic and a twisted cubic. We show this scroll is a ruled quintic surface V25\mathcal V^5_2, and study its geometric properties. The motivation in studying this scroll lies in its relationship with an Fq\mathbb F_q-subplane of PG(2,q3)PG(2,q^3) via the Bruck-Bose representation.

Keywords

Cite

@article{arxiv.1906.04319,
  title  = {A ruled quintic surface in $PG(6,q)$},
  author = {S. G. Barwick},
  journal= {arXiv preprint arXiv:1906.04319},
  year   = {2019}
}
R2 v1 2026-06-23T09:49:36.336Z