Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1
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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.
KeywordsSmooth Schubert varieties rational homogeneous manifolds variety of minimal rational tangents standard embeddings Cartan–Fubini extension
MR(2010) Subject Classification14M15 32M10 53C30
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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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