Hodge Laplacian and geometry of Kuranishi family of Fano manifolds

Autor:	Futaki, Akito, Sun, Xiaofeng, Zhang, Yingying
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematics - Algebraic Geometry Mathematics - Complex Variables 14J45 32G05 32Q15 53C55
Druh dokumentu:	Working Paper
Popis:	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 K\"ahler form remains to be a K\"ahler 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. Comment: Final version. To appear in Kyoto Journal of Mathematics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.04110 Zobrazit plný text záznamu View this record from Arxiv