On deformations of Fano manifolds

被引：2

作者：

Cao, Huai-Dong ^{[1
]}

Sun, Xiaofeng ^{[1
]}

Yau, Shing-Tung ^{[2
]}

Zhang, Yingying ^{[3
]}

机构：

[1] Lehigh Univ, Dept Math, Bethlehem, PA 18015 USA

[2] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[3] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

来源：

MATHEMATISCHE ANNALEN | 2022年 / 383卷 / 1-2期

关键词：

KAHLER-EINSTEIN METRICS; MODULI SPACE; RICCI FLOW; CURVATURE; LIMITS;

D O I：

10.1007/s00208-021-02226-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we provide new necessary and sufficient conditions for the existence of Kahler-Einstein metrics on small deformations of a Fano Kahler-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 Kahler-Einstein manifolds of general type.

引用

页码：809 / 836

页数：28

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