[Noyaux de Bergman pour une suite de métriques de solitons de Kähler–Ricci tordus]
Dans ce papier, nous montrons une conjecture due à Tian concernant une estimation 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 -Fano à singularités log terminales qui admet un soliton de Kähler–Ricci sur sa partie régulière.
In this paper, we prove the partial -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 -Fano variety which admits a Kähler–Ricci soliton on its smooth part.
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Keywords: Kähler–Einstein metrics, almost Kähler–Ricci solitons, Ricci flow, $\bar{\partial }$-equation
Mot clés : semblable banalité, autosimilarité logarithmique, loi de Gauß
@article{AIF_2017__67_3_1279_0,
author = {Jiang, Wenshuai and Wang, Feng and Zhu, Xiaohua},
title = {Bergman {Kernels} for a sequence of almost {K\"ahler{\textendash}Ricci} solitons},
journal = {Annales de l'Institut Fourier},
pages = {1279--1320},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {67},
number = {3},
year = {2017},
doi = {10.5802/aif.3110},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.3110/}
}
TY - JOUR AU - Jiang, Wenshuai AU - Wang, Feng AU - Zhu, Xiaohua TI - Bergman Kernels for a sequence of almost Kähler–Ricci solitons JO - Annales de l'Institut Fourier PY - 2017 SP - 1279 EP - 1320 VL - 67 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3110/ DO - 10.5802/aif.3110 LA - en ID - AIF_2017__67_3_1279_0 ER -
%0 Journal Article %A Jiang, Wenshuai %A Wang, Feng %A Zhu, Xiaohua %T Bergman Kernels for a sequence of almost Kähler–Ricci solitons %J Annales de l'Institut Fourier %D 2017 %P 1279-1320 %V 67 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3110/ %R 10.5802/aif.3110 %G en %F AIF_2017__67_3_1279_0
Jiang, Wenshuai; Wang, Feng; Zhu, Xiaohua. Bergman Kernels for a sequence of almost Kähler–Ricci solitons. Annales de l'Institut Fourier, Tome 67 (2017) no. 3, pp. 1279-1320. doi : 10.5802/aif.3110. http://www.numdam.org/articles/10.5802/aif.3110/
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