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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 |
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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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