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arXiv · 1704.05206

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

Shin-Young Kim·Kyeong-Dong Park
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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 $F_4$-homogeneous manifold associated to a short simple root.

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Shin-Young Kim, Kyeong-Dong Park. 2017-04-18. Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1. https://doi.org/10.1007/s10114-018-7165-z

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