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Connectedness of intersections of special Schubert varieties Sols Lucía, Ignacio Hernández, Rafael 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]. 2023-06-20T18:42:26Z 2023-06-20T18:42:26Z 1994-05 journal article 0025-2611 10.1007/BF02567610 https://hdl.handle.net/20.500.14352/58379 http://link.springer.com/article/10.1007%2FBF02567610 http://link.springer.com/ eng PB90-0637 restricted access Springer