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Journal Articles Journal of Algebra Year : 2003

The singular locus of a Schubert variety

Abstract

The singular locus of a Schubert variety Xμ in the flag variety for GLn(C) is the union of Schubert varieties Xν, where ν runs over a set Sg(μ) of permutations in Sn. We describe completely the maximal elements of Sg(μ) under the Bruhat order, thus determining the irreducible components of the singular locus of Xμ.

Dates and versions

hal-00084087 , version 1 (05-07-2006)

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Christian Kassel, Alain Lascoux, Christophe Reutenauer. The singular locus of a Schubert variety. Journal of Algebra, 2003, 269, num. 1, pp.74-108. ⟨10.1016/S0021-8693(03)00014-0⟩. ⟨hal-00084087⟩
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