Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial

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

Susan G. Barwick

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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

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

Received: 15 September 2016
Accepted: 22 October 2018
First available in Project Euclid: 26 February 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx]

projective space varieties scroll Bruck–Bose representation


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.

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