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On deformations of Fano manifolds
Mathematische Annalen ( IF 1.3 ) Pub Date : 2021-06-23 , DOI: 10.1007/s00208-021-02226-2
Huai-Dong Cao , Xiaofeng Sun , Shing-Tung Yau , Yingying Zhang

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.



中文翻译:

关于 Fano 流形的变形

在本文中,我们为 Kähler-Einstein 度量在 Fano Kähler-Einstein 流形的小变形上的存在提供了新的充分必要条件。我们还表明,Weil-Petersson 度量可以通过直接图像束上的规范\(L^2\)度量的 Ricci 曲率来近似。此外,我们描述了一般类型紧致 Kähler-Einstein 流形变形的 Kuranishi 空间上谐波映射的能量泛函的多次谐波。

更新日期:2021-06-24
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