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Hodge Laplacian and geometry of Kuranishi family of Fano manifolds

Hodge Laplacian and geometry of Kuranishi family of Fano manifolds

来源:Arxiv_logoArxiv
英文摘要

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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