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Resumen:
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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 ?(W)={??Gr l,n : ??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 ?(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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