Abstract:
We study the variation of the Mumford quotient by the action of a maximal
torus $T$ on a flag variety $G/B$ as we change the projective embedding
$G/B \hookrightarrow\mathbb P(V(\chi))$, where the $T$-linearization is
induced by the standard $G$-linearization. To do this, we describe the
linear spans of the supports of the semistable orbits. This enables us
to calculate the rank of the Picard group of the quotient $(G/B)^{ss}//T$
in the case when $G$ contains no simple components of type $A_n$.