Base subsets of Grassmannians: Infinite-dimensional case
نویسندگان
چکیده
منابع مشابه
Base subsets of polar Grassmannians
Let ∆ be a thick building of type Xn = Cn,Dn. Let also Gk be the Grassmannian of k-dimensional singular subspaces of the associated polar space Π (of rank n). We write Gk for the corresponding shadow space of type Xn,k. Every bijective transformation of Gk preserving the class of base subsets (the shadows of apartments) is a collineation of Gk, and it is induced by a collineation of Π if n 6= 4...
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Let V and V ′ be 2n-dimensional vector spaces over fields F and F ′. Let also : V × V → F and ′: V ′ × V ′ → F ′ be non-degenerate symplectic forms. Denote by and ′ the associated (2n − 1)-dimensional projective spaces. The sets of kdimensional totally isotropic subspaces of and ′ will be denoted by Gk and G ′ k , respectively. Apartments of the associated buildings intersect Gk and G ′ k by so...
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Let A be a subvariety of affine space A whose irreducible components are d-dimensional linear or affine subspaces of A. Denote by D(A) ⊂ N the set of exponents of standard monomials ofA. Using the Hilbert function, we show thatD(A) contains as many subspaces of dimension d as A contains irreducible components. We refine this result in various ways. Firstly, we specify the directions into which ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2007
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2005.10.002