Deformation rigidity of the double Cayley Grassmannian
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909630630723584 |
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| author | Kim, Shin-young Park, Kyeong-Dong |
| author_facet | Kim, Shin-young Park, Kyeong-Dong |
| contents | The double Cayley Grassmannian is a unique smooth equivariant completion with Picard number one of the 14-dimensional exceptional complex Lie group $G_2$, and it parametrizes eight-dimensional isotropic subalgebras of the complexified bi-octonions. We show the rigidity of the double Cayley Grassmannian under Kähler deformations. This means that for any smooth projective family of complex manifolds over a connected base of which one fiber is biholomorphic to the double Cayley Grassmannian, all other fibers are biholomorphic to the double Cayley Grassmannian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14331 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deformation rigidity of the double Cayley Grassmannian Kim, Shin-young Park, Kyeong-Dong Algebraic Geometry 14M27, 32G05 (Primary), 14M17, 32M12 (Secondary) The double Cayley Grassmannian is a unique smooth equivariant completion with Picard number one of the 14-dimensional exceptional complex Lie group $G_2$, and it parametrizes eight-dimensional isotropic subalgebras of the complexified bi-octonions. We show the rigidity of the double Cayley Grassmannian under Kähler deformations. This means that for any smooth projective family of complex manifolds over a connected base of which one fiber is biholomorphic to the double Cayley Grassmannian, all other fibers are biholomorphic to the double Cayley Grassmannian. |
| title | Deformation rigidity of the double Cayley Grassmannian |
| topic | Algebraic Geometry 14M27, 32G05 (Primary), 14M17, 32M12 (Secondary) |
| url | https://arxiv.org/abs/2311.14331 |