A characterization of Kempf varieties by means of standard monomials and the geometric consequences
type: Item
instance of: scholarly article
title: A characterization of Kempf varieties by means of standard monomials and the geometric consequences
zbMATH Open document ID: 0612.14049
DOI: 10.1016/0021-8693(85)90204-2
author: Craig Huneke
author: V. Lakshmibai
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: The second author introduced [in J. Indian Math. Soc., New Ser. 40, 299- 349 (1976; Zbl 0447.14014)] the name Kempf varieties for certain Schubert varieties in G/B. Here B is a Borel subgroup of the semi-simple algebraic group G and it is assumed that G is classical. It is shown in this paper that for G of type A, B or C, the Kempf varieties are exactly the Schubert varieties on which the notion ''weakly standard Young diagrams'' [introduced in the joint work of the second author, \textit{C. Musili} and \textit{C. S. Seshadri}, Proc. Indian Acad. Sci., Sect A, Part III 88, No.4, 279-362 (1979; Zbl 0447.14013)] coincides with ''standard Young diagrams'' (loc. cit.). To any Schubert variety the authors attach a poset of elements in the Weyl group. They prove that the corresponding order complex is shellable and then use this to deduce that the multicones over Kempf varieties (in G/P, P any parabolic subgroup) are normal and Cohen-Macaulay. [It has recently been proved by a quite different method that multicones over any Schubert variety always have rational singularities, see \textit{G. Kempf} and \textit{A. Ramanathan}, Invent. Math. 87, 353-363 (1987).]
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 3989554
zbMATH Keywords: standard monomials
zbMATH Keywords: Schubert varieties
zbMATH Keywords: weakly standard Young diagrams
zbMATH Keywords: multicones over Kempf varieties
reviewed by: Henning Haahr Andersen
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90204-2
OpenAlex ID: W2023770900
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description: scientific article; zbMATH DE number 3989554