The lines of PG(4, 2) are the points on a quintic in PG(9,2)

Shaw, Ron; Gordon, Neil A

Abstract

Let V denote a 5-dimensional vector space over a field, and let (bij) denote the 10 independent components of a bivectorb?Λ2Vrelative to a choice of product basis {eiΛej: 1 ≤i<j≤ 5} forΛ2V. It is well known thatb(≠ 0) is decomposable (pure, simple) if and only if its componentsbijsatisfy a set of five quadratic conditions resulting from the Grassmann relations. In the case= GF(2) it is shown that these five quadratic conditions are equivalent to a single quintic condition. In projective language the 155 lines of PG(4, 2) are therefore seen to be (in 1-1 correspondence with) the 155 points on a certain quintic lying in PG(9, 2).

Citation

Shaw, R., & Gordon, N. A. (1994). The lines of PG(4, 2) are the points on a quintic in PG(9,2). Journal of Combinatorial Theory, Series A, 68(1), 226-231. https://doi.org/10.1016/0097-3165%2894%2990102-3

• Journal Article Type: Article
• Online Publication Date: Jul 14, 2004
• Publication Date: 1994-10
• Journal: Journal of Combinatorial Theory, Series A
• Print ISSN: 0097-3165
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 68
• Issue: 1
• Pages: 226-231
• DOI: https://doi.org/10.1016/0097-3165%2894%2990102-3
• Keywords: Theoretical Computer Science; Computational Theory and Mathematics; Discrete Mathematics and Combinatorics
• Public URL: https://hull-repository.worktribe.com/output/405480
• Publisher URL: https://www.sciencedirect.com/science/article/pii/0097316594901023?via%3Dihub#!