2021/12/23 by Lins Denaux, Denaux, Lins
Mathematics · #05B25 #51E20 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2112.12452
openalex publication_date 2021/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let PG(n,q) be the Desarguesian projective space of dimension n over the finite field of order q. The linear representation of a point set K in a hyperplane at infinity of PG(n,q) is the point-line geometry consisting of the affine points of PG(n,q), together with the union of the parallel classes of affine lines corresponding to the points of K. This type of point-line geometry has been widely investigated in the literature. Curiously, if K is a subgeometry, two disguises of its linear representation occur in two separate works. In this short note, we give an explicit isomorphism between these two disguises by making use of field reduction.