Characterization of Standard Embeddings between Rational Homogeneous Manifolds of Picard Number 1

Abstract

Let X be a rational homogeneous manifold of Picard number 1. A subdiagram of the marked Dynkin diagram of X induces naturally an embedding of a rational homogeneous manifold Z into X. By a standard embedding of Z into X we will mean the composite of it with the action of an element of Aut 0 (X). In this paper, we prove a characterization of standard embeddings of Z into X by means of varieties of minimal rational tangents in the case where Z is nonlinear. We also provide a characterization of maximal linear spaces in X.