Bergman Kernels for a sequence of almost Kähler–Ricci solitons
Annales de l'Institut Fourier, Volume 67 (2017) no. 3, pp. 1279-1320.

In this paper, we prove the partial C 0 -estimate conjecture of Tian for an almost Kähler–Einstein metrics sequence of Fano manifolds, or more general, an almost Kähler–Ricci solitons sequence. This generalizes Donaldson–Sun–Tian’s result for a Kähler–Einstein metrics sequence of Fano manifolds. As an application, we prove that the Gromov–Hausdorff limit of sequence is homeomorphic to a log terminal Q-Fano variety which admits a Kähler–Ricci soliton on its smooth part.

Dans ce papier, nous montrons une conjecture due à Tian concernant une estimation C 0 partielle pour une suite de métriques de Kähler–Einstein tordues sur les variétés de Fano, ou plus généralement, pour une suite des solitons de Kähler–Ricci tordus. Ceci généralise les résultats de Donaldson–Sun–Tian pour une suite de métriques de Kähler–Einstein sur les variétés de Fano. Comme application, nous démontrons que la limite de Gromov–Hausdorff de la suite est homéomorphe à une variété de Q-Fano à singularités log terminales qui admet un soliton de Kähler–Ricci sur sa partie régulière.

Published online:
DOI: 10.5802/aif.3110
Classification: 53C25, 53C55, 58J05
Keywords: Kähler–Einstein metrics, almost Kähler–Ricci solitons, Ricci flow, $\bar{\partial }$-equation
Jiang, Wenshuai 1; Wang, Feng 1; Zhu, Xiaohua 2

1 School of Mathematical Sciences, Zhejiang University, Zheda Road 38, Hangzhou, Zhejiang, 310027, P.R. China
2 School of Mathematical Sciences and BICMR, Peking University, Beijing, 100871, P.R. China
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jiang, Wenshuai; Wang, Feng; Zhu, Xiaohua. Bergman Kernels for a sequence of almost Kähler–Ricci solitons. Annales de l'Institut Fourier, Volume 67 (2017) no. 3, pp. 1279-1320. doi : 10.5802/aif.3110.

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