A geometric approach to alternating k-linear forms

被引:1
|
作者
Cardinali, Ilaria [1 ]
Giuzzi, Luca [2 ]
Pasini, Antonio [1 ]
机构
[1] Univ Siena, Dept Informat Engn & Math, Via Roma 56, I-53100 Siena, Italy
[2] Univ Brescia, DICATAM Sect Math, Via Branze 53, I-25123 Brescia, Italy
关键词
Grassmann geometry; Hyperplane; Multilinear form; Alternating form; HYPERPLANES;
D O I
10.1007/s10801-016-0730-6
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Denote by Gk (V) the Grassmannian of the k-subspaces of a vector space V over a field K. There is a natural correspondence between hyperplanes H of Gk (V) and alternating k-linear forms on V defined up to a scalar multiple. Given a hyperplane H of Gk (V), we define a subspace R up arrow(H) of G(k-1)(V) whose elements are the (k-1)subspaces A such that all k-spaces containing A belong to H. When n - k is even, R up arrow(H) might be empty; when n - k is odd, each element of G(k-2)(V) is contained in at least one element of R.(H). In the present paper, we investigate several properties of R up arrow(H), settle some open problems and propose a conjecture.
引用
收藏
页码:931 / 963
页数:33
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