Fano manifolds with weak almost Kähler-Ricci solitons

2013/07/31 by Xiaohua Zhu, Zhu, Xiaohua
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1307.8226

openalex publication_date 2013/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that a sequence of weak almost Kähler-Ricci solitons under further suitable conditions converge to a Kähler-Ricci soliton with complex codimension of singularities at least 2 in the Gromov-Hausdorff topology. As a corollary, we show that on a Fano manifold with the modified K-energy bounded below, there exists a sequence of weak almost Kähler-Ricci solitons which converge to a Kähler-Ricci soliton with complex codimension of singularities at least 2 in the Gromov-Hausdorff topology.

Citations

• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• K-stability and Kähler-Einstein metrics

Related

• Compactness of Kahler-Ricci solitons on Fano manifolds
• The moduli space of Fano manifolds with Kähler-Ricci solitons
• Bergman Kernels and algebraic structure of limit space for a sequence of almost Kähler-Ricci solitons
• Degeneration of Kahler-Ricci solitons on Fano manifolds
• Generalized almost-Kähler-Ricci solitons