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Variation of Mumford's quotients for the maximal torus action on a flag variety

Vladimir S. Zhgoon
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Abstract

We study a variation of Mumford's quotient for the action of a maximal torus $T$ on a flag variety $G/B$ depending on projective embedding $G/B \hookrightarrow \Bbb P(V(χ))$, where $T$-linearization is induced by the standard $G$-linearization. We describe the linear spans of the supports of semistable orbits, that allow us to calculate the rank of the Picard group of quotient $(G/B)^{ss}//T$, when $G$ does not contain simple factors of type $A_n$.

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Vladimir S. Zhgoon. 2006-09-30. Variation of Mumford's quotients for the maximal torus action on a flag variety. https://arxiv.org/abs/math/0610014

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