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

S. Senthamarai Kannan (), Arpita Nayek () and Pinakinath Saha ()
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S. Senthamarai Kannan: Chennai Mathematical Institute
Arpita Nayek: Chennai Mathematical Institute
Pinakinath Saha: Tata Inst. of Fundamental Research

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 1, 273-293

Abstract: 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 .

Keywords: Line bundle; Grassmannian; Schubert variety; Semistable points; GIT-quotient; 14M15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00017-8

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