A Schubert variety of a
rational homogeneous manifold A normal variety with an
action of a reductive group is said to be horospherical
if it has an open dense orbit which is a torus bundle over a rational
homogenous manifold. Up to now all known examples of smooth Schubert
varieties are horospherical. In this talk, we show
that a smooth Schubert variety of a rational homogeneous manifold of Picard
number one is horospherical and determine all
smooth Schubert varieties of rational homogeneous manifolds of Picard number
one. |