Variation of Mumford quotients by torus actions on full flag varieties. I

摘要

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 -> 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..