Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866911718716735488 |
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| author | Chen, Yifei Fu, Baohua Li, Qifeng |
| author_facet | Chen, Yifei Fu, Baohua Li, Qifeng |
| contents | 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 $X(\mathbb{A})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_02799 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras Chen, Yifei Fu, Baohua Li, Qifeng Algebraic Geometry 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 $X(\mathbb{A})$. |
| title | Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2212.02799 |