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Schubert Unions in Grassmann Varieties

Johan P. Hansen·Trygve Johnsen·Kristian Ranestad
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Abstract

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.

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Johan P. Hansen, Trygve Johnsen, Kristian Ranestad. 2005-03-07. Schubert Unions in Grassmann Varieties. https://arxiv.org/abs/math/0503121

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