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

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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 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 Aₙ.