Schubert Unions in Grassmann Varieties
代数几何
2007-05-23 v1 组合数学
摘要
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.
引用
@article{arxiv.math/0503121,
title = {Schubert Unions in Grassmann Varieties},
author = {Johan P. Hansen and Trygve Johnsen and Kristian Ranestad},
journal= {arXiv preprint arXiv:math/0503121},
year = {2007}
}
备注
37 pages, 2 figures