Torus quotients of Schubert varieties in the Grassmannian $G_{2,n}$
| Autor: | Kannan, S. Senthamarai, Nayek, Arpita, Saha, Pinakinath |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Indian Journal of Pure and Applied Mathematics (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s13226-021-00017-8 |
| Popis: | Let $G=SL(n, \mathbb{C}),$ 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 $G_{2,n}.$ We prove that the GIT quotients of the Richardson varieties in the minimal dimensional Schubert variety admitting stable points in $G_{2,n}$ are projective spaces. Further, we prove that the GIT quotients of certain Richardson varieties in $G_{2,n}$ are projective toric varieties. Also, we prove that the GIT quotients of the Schubert varieties in $G_{2,n}$ have at most finite set of singular points. Further, we have computed the exact number of singular points of the GIT quotient of $G_{2,n}.$ Comment: 24 pages |
| Databáze: | arXiv |
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