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- W4286870046 abstract "Let $G=SL(2n,mathbb{C})$ $(n geq 3)$ and $T$ be a maximal torus in $G.$ In this article, we study the GIT quotients of the Schubert varieties in $G_{n,2n}$ for the action of $T.$ We show that there exists a Schubert variety $X(v)$ in $G_{n,2n}$ admitting semistable point such that the GIT quotient of $X(v)$ is not projectively normal with respect to the descent of the ample line bundle $mathcal{L}(2omega_{n})$. As a consequence, we conclude that for any Schubert variety $X(w)$ in $G_{n,2n}$ containing $X(v),$ the GIT quotient of $X(w)$ is not projectively normal with respect to the descent of the ample line bundle $mathcal{L}(2omega_{n}).$ In particular, the GIT quotient of $G_{n,2n}$ ($nge 3$) is not projectively normal with respect to the descent of the ample line bundle $mathcal{L}(2omega_{n}).$" @default.
- W4286870046 created "2022-07-25" @default.
- W4286870046 creator A5010537615 @default.
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- W4286870046 date "2021-11-01" @default.
- W4286870046 modified "2023-09-30" @default.
- W4286870046 title "Torus quotients of Schubert varieties in the Grassmannian $G_{n,2n}$" @default.
- W4286870046 doi "https://doi.org/10.48550/arxiv.2111.00802" @default.
- W4286870046 hasPublicationYear "2021" @default.
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