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Torus quotients of Schubert varieties in the Grassmannian $$G_{2, n}$$ G 2 , n

Author

Listed:
  • S. Senthamarai Kannan

    (Chennai Mathematical Institute)

  • Arpita Nayek

    (Chennai Mathematical Institute)

  • Pinakinath Saha

    (Tata Inst. of Fundamental Research)

Abstract

Let $$G=SL(n, {\mathbb {C}}),$$ G = S L ( n , C ) , and T be a maximal torus of G, where n is a positive even integer. In this article, we study the GIT quotients of the Schubert varieties in the Grassmannian $$G_{2,n}.$$ G 2 , n . We prove that the GIT quotients of the Richardson varieties in the minimal dimensional Schubert variety admitting stable points in $$G_{2,n}$$ G 2 , n are projective spaces (see Proposition 3.5 and Proposition 3.6). Further, we prove that the GIT quotients of certain Richardson varieties in $$G_{2,n}$$ G 2 , n are projective toric varieties. Also, we prove that the GIT quotients of the Schubert varieties in $$G_{2,n}$$ G 2 , n have at most finite set of singular points. Further, we have computed the exact number of singular points of the GIT quotient of $$G_{2,n}.$$ G 2 , n .

Suggested Citation

  • S. Senthamarai Kannan & Arpita Nayek & Pinakinath Saha, 2022. "Torus quotients of Schubert varieties in the Grassmannian $$G_{2, n}$$ G 2 , n," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(1), pages 273-293, March.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:1:d:10.1007_s13226-021-00017-8
    DOI: 10.1007/s13226-021-00017-8
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