%0 Journal Article
%A Sols Lucía, Ignacio
%A Hernández, Rafael
%T Connectedness of intersections of special Schubert varieties
%D 1994
%@ 0025-2611
%U https://hdl.handle.net/20.500.14352/58379
%X Let Gr l,n   be the Grassmann variety of l -dimensional subspaces of an n -dimensional vector space V  over an algebraically closed field k . Let σ(W)={Λ∈Gr l,n : Λ∩W≠0}  denote the special Schubert variety associated to a subspace W  of V . The main theorem of the paper is the following: The intersection ⋂ m j=1 σ(V j )  of the special Schubert   varieties  associated to  subspaces V j  , j=1,2,⋯,m , of dimension n−l−a j +1  such that l(n−l)−∑ m j=1 a j >0  is connected. Moreover, the intersection is irreducible of dimension l(n−l)−∑ m j=1 a j   for a general choice of V j  . The  authors conjecture  that the irreducibility holds for intersections of arbitrary Schubert varieties, when they are in general position with nonempty intersection.  For a related connectivity result the authors refer to a paper of J. P. Hansen [Amer. J. Math. 105 (1983), no. 3, 633–639].
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