Projective normality of torus quotients of flag varieties

Abstract

Let G=SLn(C) and T be a maximal torus in G. We show that the quotient T\\\\G/Pα1∩Pα2 is projectively normal with respect to the descent of a suitable line bundle, where Pαi is the maximal parabolic subgroup in G associated to the simple root αi, i=1,2. We give a degree bound of the generators of the homogeneous coordinate ring of T\\\\(G3,6)Tss(L2ϖ3). If G=Spin7, we give a degree bound of the generators of the homogeneous coordinate ring of T\\\\(G/Pα2)Tss(L2ϖ2) whereas we prove that the quotient T\\\\(G/Pα3)Tss(L4ϖ3) is projectively normal with respect to the descent of the line bundles L4ϖ3.