Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1

摘要

Smooth Schubert varieties in rational homogeneous manifolds of Picard number1 are horospherical varieties. We characterize standard embeddings of smoothSchubert varieties in rational homogeneous manifolds of Picard number 1 bymeans of varieties of minimal rational tangents. In particular, we mainlyconsider nonhomogeneous smooth Schubert varieties in symplectic Grassmanniansand in the 20-dimensional $F_4$-homogeneous manifold associated to a shortsimple root.