The GIT quotient of the minimal Schubert variety X(w_{r,n}) modulo the subtorus T_{J_r} is isomorphic to the total space of the r-th stage of an iterated projective space bundle over P^{q-1}.
Math.143(5)(2007), 1255- 1312
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GIT quotient of minimal dimensional Schubert variety modulo a subtorus
The GIT quotient of the minimal Schubert variety X(w_{r,n}) modulo the subtorus T_{J_r} is isomorphic to the total space of the r-th stage of an iterated projective space bundle over P^{q-1}.