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

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 $G/B\hookrightarrow \mathbb{P}(V(\chi ))$, 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 $A_n$.

arXiv comment15 pages, 5 figures