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arXiv · 2212.02799

Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras

Yifei Chen·Baohua Fu·Qifeng Li
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Abstract

To each complex composition algebra $\mathbb{A}$, there associates a projective symmetric manifold $X(\mathbb{A})$ of Picard number one, which is just a smooth hyperplane section of the following varieties ${\rm Lag}(3,6), {\rm Gr}(3,6), \mathbb{S}_6, E_7/P_7.$ In this paper, it is proven that these varieties are rigid, namely for any smooth family of projective manifolds over a connected base, if one fiber is isomorphic to $X(\mathbb{A})$, then every fiber is isomorphic to $X(\mathbb{A})$.

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Yifei Chen, Baohua Fu, Qifeng Li. 2022-12-06. Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras. https://doi.org/10.46298/epiga.2023.10432

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