2005/03/07 by Johan P. Hansen, Hansen, Johan P., Trygve Johnsen +3
Mathematics · #14M15 (05E15 #94B27) #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO #msc:14M15
paper · pdf · doi:10.48550/arxiv.math/0503121
37 pages, 2 figures
arxiv created 2005/03/07 · arxiv updated 2009/12/01
We study subsets of Grassmann varieties G(l,m) over a field F, such that these subsets are unions of Schubert cycles, with respect to a fixed flag. We study the linear spans of, and in case of positive characteristic, the number of points on such unions over finite fields. Moreover we study a geometric duality of such unions, and give a combinatorial interpretation of this duality. We discuss the maximum number of points over a finite field for the Schubert unions of a given spanning dimension, and we give some applications to coding theory. We define Schubert union codes, and study the parameters and support weights of these codes and of the well-known Grassmann codes.