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

Abstract

Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional $F_4$-homogeneous manifold associated to a short simple root.

22 pages

References in corpus (3)

• Billey-Postnikov decompositions and the fibre bundle structure of Schubert varieties
• Geometric structures modeled on smooth projective horospherical varieties of Picard number one
• Rigidity of smooth Schubert varieties in a rational homogeneous manifold associated to a short root

Cited by in corpus (1)

• Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one