Vol. 17, No. 1, 2019

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

Susan G. Barwick

Vol. 17 (2019), No. 1, 25–41

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 V25, and study its geometric properties. The motivation in studying this scroll lies in its relationship with an Fq-subplane of PG(2,q3) via the Bruck–Bose representation.

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projective space, varieties, scroll, Bruck–Bose representation
Mathematical Subject Classification 2010
Primary: 51E20
Received: 15 September 2016
Accepted: 22 October 2018
Published: 19 November 2018
Susan G. Barwick
School of Mathematical Sciences
University of Adelaide