Multiplicities of Singular Points in Schubert Varieties of Grassmannians

Victor Kreiman and V. Lakshmibai

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 553-563 from Springer

Abstract: Abstract We give a closed-form formula for the Hilbert function of the tangent cone at the identity of a Schubert variety X in the Grassmannian in both group theoretic and combinatorial terms. We also give a formula for the multiplicity of X at the identity, and a Gröbner basis for the ideal defining X(w) ∩ O − as a closed subvariety of O −, where O − is the opposite cell in the Grassmannian. We give conjectures for the Hilbert function and multiplicity at points other than the identity.

Keywords: Singular Point; Lexicographic Order; Tangent Cone; Hilbert Series; Hilbert Function (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_31

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DOI: 10.1007/978-3-642-18487-1_31

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