## Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial

### Ruled quintic surfaces in $\mathrm{PG}(6,q)$

Susan G. Barwick

#### Abstract

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 $V 2 5$, and study its geometric properties. The motivation in studying this scroll lies in its relationship with an $F q$-subplane of $PG ( 2 , q 3 )$ via the Bruck–Bose representation.

#### Article information

Source
Innov. Incidence Geom. Algebr. Topol. Comb., Volume 17, Number 1 (2019), 25-41.

Dates
Accepted: 22 October 2018
First available in Project Euclid: 26 February 2019

https://projecteuclid.org/euclid.iig/1551206773

Digital Object Identifier
doi:10.2140/iig.2019.17.25

Mathematical Reviews number (MathSciNet)
MR3986545

Zentralblatt MATH identifier
1403.51005

#### Citation

Barwick, Susan G. Ruled quintic surfaces in $\mathrm{PG}(6,q)$. Innov. Incidence Geom. Algebr. Topol. Comb. 17 (2019), no. 1, 25--41. doi:10.2140/iig.2019.17.25. https://projecteuclid.org/euclid.iig/1551206773

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