Projective normality of torus quotients of flag varieties

2019/06/24 by Nayek, Arpita, Pattanayak, Santosha Kumar, Jindal, Shivang
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1906.09759

Abstract

Let G=SL_n(\mathbb C) and T be a maximal torus in G. We show that the quotient T \backslash \backslash G/P_α1∩ P_α2 is projectively normal with respect to the descent of a suitable line bundle, where P_αi is the maximal parabolic subgroup in G associated to the simple root α_i, i=1,2. We give a degree bound of the generators of the homogeneous coordinate ring of T \backslash \backslash (G_3,6)^ss_T(L_2\varpi3). If G =Spin₇, we give a degree bound of the generators of the homogeneous coordinate ring of T \backslash \backslash (G/P_α2)^ss_T(L_2\varpi2) whereas we prove that the quotient T\backslash\backslash (G/P_α3)^ss_T(L_4\varpi3) is projectively normal with respect to the descent of the line bundles L_4\varpi3.

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