Multiplicities of Singular Points in Schubert Varieties of Grassmannians

2001/08/09 by Victor Kreiman, V. Kreiman, Kreiman, V. +2
Mathematics · #14M15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #math.AG #msc:14M15

paper · pdf · doi:10.48550/arxiv.math/0108071

11 pages

arxiv created 2001/08/09 · openalex publication_date 2001/08/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Grobner basis for the ideal defining the intersection of X with the opposite cell as a closed subvariety of the opposite cell. We give conjectures for the Hilbert function and multiplicity at points other than the identity.

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• Multiplicities of Points on Schubert Varieties in Grassmannians
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• Hilbert functions of points on Schubert varieties in the Grassmannian
• The multiplicity of a singularity in a vexillary Schubert variety