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Smooth torus quotients of Schubert varieties in the Grassmannian

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Abstract

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 \({{{\mathcal {L}}}}\). We give necessary and sufficient combinatorial conditions for the GIT quotient \(T\backslash \hspace{-3.33328pt}\backslash X(w)^{ss}_{T}({{{\mathcal {L}}}})\) to be smooth.

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Notes

  1. rows are numbered \(1, \ldots , r\) from bottom to top.

  2. the notation we use is different from theirs, they work with non-increasing sequences

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Authors and Affiliations

  1. Tata Institute of Fundamental Research, Mumbai, India

    Sarjick Bakshi

  2. Chennai Mathematical Institute, Chennai, India

    S. Senthamarai Kannan & K. Venkata Subrahmanyam

Authors
  1. Sarjick Bakshi
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  2. S. Senthamarai Kannan
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  3. K. Venkata Subrahmanyam
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Correspondence to Sarjick Bakshi.

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Communicated by Indranil Biswas.

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Bakshi, S., Kannan, S.S. & Subrahmanyam, K.V. Smooth torus quotients of Schubert varieties in the Grassmannian. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00549-9

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