The cubic Segre variety in PG(5,2)

Shaw, Ron; Gordon, Neil A.

Abstract

The Segre variety S 1,2 in PG(5, 2) is a 21-set of points which is shown to have a cubic equation Q(x) = 0. If T(x, y, z) denotes the alternating trilinear form obtained by completely polarizing the cubic polynomial Q, then the associate U # of an r-flat U ⊂ PG (5, 2) is defined to be U# = z ∈ PG (5, 2), T(u1, u2, z) = 0, for, all, u1, u-2in U, and so is an s-flat for some s. Those lines L of PG(5, 2) which are singular, satisfying that is L # = PG(5.2), are shown to form a complete spread of 21 lines. For each r-flat U ⊂ PG (5, 2) its associate U # is determined. Examples are given of four kinds of planes P which are self-associate, P # = P, and three kinds of planes for which P, P # , P ## are disjoint planes such that P ### = P. © 2008 Springer Science+Business Media, LLC.

Citation

Shaw, R., & Gordon, N. A. (2009). The cubic Segre variety in PG(5,2). Designs, codes, and cryptography, 51(2), 141-156. https://doi.org/10.1007/s10623-008-9250-2

• Journal Article Type: Article
• Online Publication Date: Dec 4, 2008
• Publication Date: 2009-05
• Deposit Date: Nov 13, 2014
• Journal: Designs Codes And Cryptography
• Print ISSN: 0925-1022
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 51
• Issue: 2
• Pages: 141-156
• DOI: https://doi.org/10.1007/s10623-008-9250-2
• Keywords: Applied Mathematics; Computer Science Applications
• Public URL: https://hull-repository.worktribe.com/output/460081
• Contract Date: Nov 13, 2014