Hodge Laplacian and geometry of Kuranishi family of Fano manifolds
Hodge Laplacian and geometry of Kuranishi family of Fano manifolds
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.
Akito Futaki、Xiaofeng Sun、Yingying Zhang
数学
Akito Futaki,Xiaofeng Sun,Yingying Zhang.Hodge Laplacian and geometry of Kuranishi family of Fano manifolds[EB/OL].(2025-07-24)[2025-08-06].https://arxiv.org/abs/2212.04110.点此复制
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