Torus Quotients of Richardson Varieties

2023/06/27 by Somnath Dake, Shripad M. Garge, Dake, Somnath +3
Mathematics · #14M15 #14M17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2306.15323

openalex publication_date 2023/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For 1≤ r≤ n-1, let G_r,n denote the Grassmannian parametrizing r-dimensional subspaces of ℂⁿ. Let (r,n)=1. In this article we show that the GIT quotients of certain Richardson varieties in G_r,n for the action of a maximal torus in SL(n,ℂ) are the product of projective spaces with respect to the descent of a suitable line bundle.

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