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

作　　者：Shin-Young KIM Kyeong-Dong PARK 

机构地区：[1]Department of Mathematics and Statistics, Masaryk University, Brno, Czech [2]Center for Geometry and Physics, Institute for Basic Science ( IBS), Pohang, Korea

出　　处：《Acta Mathematica Sinica,English Series》2018年第3期466-487,共22页数学学报（英文版）

基　　金：supported by the National Researcher Program 2010-0020413 of NRF;GA17-19437S of Czech Science Foundation(GACR);partially supported by the Simons-Foundation grant 346300;the Polish Government MNi SW 2015-2019 matching fund;supported by BK21 PLUS SNU Mathematical Sciences Division;IBS-R003-Y1

摘　　要：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.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.

关 键 词：Smooth Schubert varieties rational homogeneous manifolds variety of minimal rational tangents standard embeddings Cartan-Fubini extension 

分 类 号：O[理学]