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arXiv · 1412.7598

Admissible pairs of Hermitian symmetric spaces in the perspective of the theory of varieties of minimal rational tangents

Yunxin Zhang
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Abstract

We study a pair (\mathcal{S}_0,\mathcal{S}) of irreducible Hermitian Symmetric Spaces of compact type (cHSS) in this paper, with the first aim being classifying all the admissible pairs (\mathcal{S}_0,\mathcal{S})). This notion is a natural generalization of the pairs of sub-diagram type originated by Jaehyun Hong and Ngaiming Mok ([HoM 10]). Based on this classification, we partially solve the rigidity problem for the admissible pairs (\mathcal{S}_0,\mathcal{S}) which was raised by Mok and Zhang (2014) ([MoZ 14]), culminating in determining a sufficient condition for the pairs being non-rigid and proving that special pairs, which show up in the classification procedure, are algebraic, as a weaker result than being rigid. However, whether special pairs are rigid or not remains unknown and needs further investigation in the framework of VMRT theory.

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Yunxin Zhang. 2014-12-24. Admissible pairs of Hermitian symmetric spaces in the perspective of the theory of varieties of minimal rational tangents. https://arxiv.org/abs/1412.7598

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