A ruled quintic surface in PG(6,q)

2019/06/04 by S. G. Barwick, Barwick, S. G.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1906.04319

openalex publication_date 2019/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we look at a scroll of PG(6,q) that uses a projectivity to rule a conic and a twisted cubic. We show this scroll is a ruled quintic surface \mathcal V⁵₂, and study its geometric properties. The motivation in studying this scroll lies in its relationship with an \mathbb F_q-subplane of PG(2,q³) via the Bruck-Bose representation.

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