Jaehyun Hong, Seoul National University, Korea

Characterization of a Smooth Schubert Variety

Abstract

Geometric structures on a Fano manifold of Picard number one defined by the variety of minimal rational tangents have been studied by Hwang and Mok in a series of works. On a rational homogeneous manifold G/P of Picard number one it is defined by the space of tangent directions to lines contained in G/P after we consider G/P as a projective manifold by the first canonical embedding. In this talk we will consider the geometric structure on a smooth Schubert variety in a rational homogeneous manifold of Picard number one, defined by the space of tangent directions to lines contained in it. Using this geometric structure we will give a characterization of a smooth Schubert variety of a rational homogeneous manifold of Picard number one. This is a joint work with N. Mok.