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On deformations of Fano manifolds

Huai-Dong Cao Department of Mathematics, Lehigh University, Bethlehem, PA, 18015, USA Xiaofeng Sun Department of Mathematics, Lehigh University, Bethlehem, PA, 18015, USA Shing-Tung Yau Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA Yingying Zhang Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

Differential Geometry mathscidoc:2204.10002

Mathematische Annalen, 2021.6
In this paper, we provide new necessary and sufficient conditions for the existence of Kähler–Einstein metrics on small deformations of a Fano Kähler–Einstein manifold. We also show that the Weil–Petersson metric can be approximated by the Ricci curvatures of the canonical L^2 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 Kähler–Einstein manifolds of general type.
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@inproceedings{huai-dong2021on,
  title={On deformations of Fano manifolds},
  author={Huai-Dong Cao, Xiaofeng Sun, Shing-Tung Yau, and Yingying Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428134027755529138},
  booktitle={Mathematische Annalen},
  year={2021},
}
Huai-Dong Cao, Xiaofeng Sun, Shing-Tung Yau, and Yingying Zhang. On deformations of Fano manifolds. 2021. In Mathematische Annalen. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428134027755529138.
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