Connectedness of intersections of special Schubert varieties

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Sols, Ignacio and Hernández, Rafael (1994) Connectedness of intersections of special Schubert varieties. Manuscripta mathematica, 83 (2). pp. 215-222. ISSN 0025-2611

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Official URL: http://link.springer.com/article/10.1007%2FBF02567610




Abstract

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].


Item Type:Article
Uncontrolled Keywords:Divisors
Subjects:Sciences > Mathematics > Algebra
ID Code:20572
Deposited On:22 Mar 2013 14:13
Last Modified:06 Sep 2018 14:38

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