Hodge Laplacian and geometry of Kuranishi family of Fano manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911073247952896 |
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| author | Futaki, Akito Sun, Xiaofeng Zhang, Yingying |
| author_facet | Futaki, Akito Sun, Xiaofeng Zhang, Yingying |
| contents | We first obtain eigenvalue estimates for the Hodge Laplacian on Fano manifolds, which follow from the Bochner-Kodaira formula. Then we apply it to study the geometry of the Kuranishi family of deformations of Fano manifolds. We show that the original Kähler form remains to be a Kähler form for other members of the Kuranishi family, and give an explicit formula of the Ricci potential. We also show that our set-up gives another account for the Donaldson-Fujiki picture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_04110 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hodge Laplacian and geometry of Kuranishi family of Fano manifolds Futaki, Akito Sun, Xiaofeng Zhang, Yingying Differential Geometry Algebraic Geometry Complex Variables 14J45, 32G05, 32Q15, 53C55 We first obtain eigenvalue estimates for the Hodge Laplacian on Fano manifolds, which follow from the Bochner-Kodaira formula. Then we apply it to study the geometry of the Kuranishi family of deformations of Fano manifolds. We show that the original Kähler form remains to be a Kähler form for other members of the Kuranishi family, and give an explicit formula of the Ricci potential. We also show that our set-up gives another account for the Donaldson-Fujiki picture. |
| title | Hodge Laplacian and geometry of Kuranishi family of Fano manifolds |
| topic | Differential Geometry Algebraic Geometry Complex Variables 14J45, 32G05, 32Q15, 53C55 |
| url | https://arxiv.org/abs/2212.04110 |