Acta Mathematica Sinica, English Series

, Volume 34, Issue 3, pp 466–487 | Cite as

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

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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 F4-homogeneous manifold associated to a short simple root.

Keywords

Smooth Schubert varieties rational homogeneous manifolds variety of minimal rational tangents standard embeddings Cartan–Fubini extension 

MR(2010) Subject Classification

14M15 32M10 53C30 

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Notes

Acknowledgements

In October–November 2016, Workshop and International Conference on Spherical Varieties organized by Michel Brion and Baohua Fu were held in Sanya. This work had progressed while attending the workshop. The authors would like to thank the organizers for their invitation and Tsinghua Sanya International Mathematics Forum for the support and hospitality. They warmly thank Jaehyun Hong and Jun-Muk Hwang for the discussions on this topic and the useful comments. They also thank the referees for pointing out ambiguities and giving helpful comments.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic
  2. 2.Center for Geometry and PhysicsInstitute for Basic Science (IBS)PohangKorea

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