On Deformations of Fano Manifolds
Differential Geometry
2024-03-12 v2
Abstract
In this paper we provide new necessary and sufficient conditions for the existence of K\"ahler-Einstein metrics on small deformations of a Fano K\"ahler-Einstein manifold. We also show that the Weil-Petersson metric can be approximated by the Ricci curvatures of the canonical metrics on the direct image bundles. In addition, we describe the plurisubharmonicity of the energy functional of harmonic maps on the Kuranishi space of the deformation of compact K\"ahler-Einstein manifolds of general type.
Keywords
Cite
@article{arxiv.2006.01355,
title = {On Deformations of Fano Manifolds},
author = {Huai-Dong Cao and Xiaofeng Sun and Shing-Tung Yau and Yingying Zhang},
journal= {arXiv preprint arXiv:2006.01355},
year = {2024}
}
Comments
A new equivalent condition has been added to Theorem 1.1. In Theorem 1.2, we removed the assumption on the automorphism group which appeared in the previous version