Singular loci of varieties of complexes
type: Item
instance of: scholarly article
title: Singular loci of varieties of complexes
zbMATH Open document ID: 0982.14027
DOI: 10.1016/S0022-4049(99)00144-9
published in: Journal of Pure and Applied Algebra
publication date: 2002-03-21T00:00:00Z
review text: Let \(M(l\times m)\) be the affine space of matrices over a field with \(l\) rows and \(m\) columns. Denote by \(V\) the algebraic set consisting of those pairs \((A_1, A_2)\) in \(M(n_2\times n_1) \times M(n_3\times n_2)\) such that \(A_2A_1=0\). Then each irreducible component of \(V\) is isomorphic to the opposite cell in a Schubert variety \(SL(n_1+n_2+n_3)/Q\) where \(Q\) is a parabolic group. In this article the singular locus of each irreducible component of \(V\) is determined. A conjecture of Lakshmibai and Sandhya on how to write the singular locus of the associated Schubert variety \(X(\nu) =\overline{B\nu B} \pmod B\) of \(C\) as a union of varieties \(X(\lambda)\) is also proved.
reviewed by: Dan Laksov
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 1517302
zbMATH Keywords: singular loci
zbMATH Keywords: varieties of complexes
zbMATH Keywords: Schubert varieties
author: V. Lakshmibai
MaRDI profile type: Publication
cites work: Degeneracy Schemes and Schubert Varieties
cites work: Criterion for smoothness of Schubert varieties in Sl(n)/B
cites work: Geometry of G/P-II [The work of De Concini and Procesi and the basic conjectures]
cites work: Schubert polynomials and the Littlewood-Richardson rule
cites work: Q3682606
Wikidata QID: Q127517355
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description: scientific article; zbMATH DE number 1517302