Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torus quotients of Schubert varieties in the Grassmannian $G_{n,2n}$   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 $\mathcal{L}(2\omega_{n})$. 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 $\mathcal{L}(2\omega_{n}).$ In particular, the GIT quotient of
$G_{n,2n}$ ($n\ge 3$) is not projectively normal with respect to the descent of
the ample line bundle $\mathcal{L}(2\omega_{n}).$

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org