Torus quotients of homogeneous spaces-minimal dimensional Schubert Variety admitting semi-stable points

Abstract

In this paper, for any simple, simply connected algebraic group $G$ of type $B_n,C_n$ or $D_n$ and for any maximal parabolic subgroup $P$ of $G$, we describe all minimal dimensional Schubert varieties in $G/P$ admitting semistable points for the action of a maximal torus $T$ with respect to an ample line bundle on $G/P$. In this paper, we also describe, for any semi-simple simply connected algebraic group $G$ and for any Borel subgroup $B$ of $G$, all Coxeter elements $τ$ for which the Schubert variety $X(τ)$ admits a semistable point for the action of the torus $T$ with respect to a non-trivial line bundle on $G/B$.