2014/01/25 by Wenshuai Jiang, Feng Wang, Jiang, Wenshuai +3
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1401.6542
In this paper, we give a lower bound of Bergman kernels for a sequence of almost Kähler-Einstein Fano manifolds, or more general, a sequence of Fano manifolds with almost Kähler-Ricci solitons. This generalizes a result by Donaldson-Sun, Tian for Kähler-Einstein manifolds sequence with positive scalar curvature. As an application of our result, we prove that the Gromov-Hausdorff limit of sequence is homomorphic to a log terminal Q-Fano variety which admits a Kähler-Ricci soliton on its smooth part.