2013/03/22 by Ilaria Cardinali, Cardinali, Ilaria, Antonio Pasini +1
Computer Science · Engineering · Mathematics · #14J25 #14J26 #51A45 #Advanced Graph Theory Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1303.5609
openalex publication_date 2013/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An embedding of a point-line geometry Γis usually defined as an injective mapping εfrom the point-set of Γto the set of points of a projective space such that ε(l) is a projective line for every line l of Γ, but different situations have lately been considered in the literature, where ε(l) is allowed to be a subline of a projective line or a curve. In this paper we propose a more general definition of embedding which includes all the above situations and we focus on a class of embeddings, which we call Grassmman embeddings, where the points of Γare firstly associated to lines of a projective geometry PG(V), next they are mapped onto points of PG(V\wedge V) via the usual projective embedding of the line-grassmannian of PG(V) in PG(V\wedge V). In the central part of our paper we study sets of points of PG(V\wedge V) corresponding to lines of PG(V) totally singular for a given pseudoquadratic form of V. Finally, we apply the results obtained in that part to the investigation of Grassmann embeddings of several generalized quadrangles.