Smooth torus quotients of Schubert varieties in the Grassmannian

Let \(r < n\) be positive integers and further suppose \(r\) and \(n\) are coprime. We study the GIT quotient of Schubert varieties \(X(w)\) in the Grassmannian \(G_{r,n}\), admitting semistable points for the action of \(T\) with respect to the \(T\)-linearized line bundle \({\cal L}(n\omega_r)\...

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Bibliographic Details
Published in:arXiv.org 2019-12
Main Authors: Bakshi, Sarjick, Kannan, S Senthamarai, Subrahmanyam, K Venkata
Format: Article
Language:English
Subjects:
Combinatorial analysis
Quotients
Toruses
Online Access:Get full text
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Summary:Let \(r < n\) be positive integers and further suppose \(r\) and \(n\) are coprime. We study the GIT quotient of Schubert varieties \(X(w)\) in the Grassmannian \(G_{r,n}\), admitting semistable points for the action of \(T\) with respect to the \(T\)-linearized line bundle \({\cal L}(n\omega_r)\). We give necessary and sufficient combinatorial conditions for the GIT quotient \(T\backslash\mkern-6mu\backslash X(w)^{ss}_{T}({\cal L}(n\omega_r))\) to be smooth.
ISSN:2331-8422