Geodesic
Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras
Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023)

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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 $X(\mathbb{A})$.
DOI : 10.46298/epiga.2023.10432
Classification : 14J45, 14M27, 32G10 
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     author = {Chen, Yifei and Fu, Baohua and Li, Qifeng},
     title = {Rigidity of projective symmetric manifolds of {Picard} number 1 associated to composition algebras},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     year = {2023},
     doi = {10.46298/epiga.2023.10432},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.10432/}
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Chen, Yifei; Fu, Baohua; Li, Qifeng. Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras. Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023). doi: 10.46298/epiga.2023.10432

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