Year: 2025
Type: article
Abstract: 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 a Kähler form for other members of the Kuranishi family, and we give an explicit formula of the Ricci potential. We also show that our setup gives another account for the Donaldson–Fujiki picture.
Source: Kyoto journal of mathematics
Authors: Akito Futaki, Xiaofeng Sun, Yingying Zhang
Institutions: Tsinghua University, Lehigh University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4952392286
OpenAlex ID: W4413297357