Existence of Kahler-Ricci solitons on smoothable Q-Fano varities

2019/08/27 by Yan Li, Li, Yan
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1908.10091

openalex publication_date 2019/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we prove the existence of Kahler-Ricci solitons on smoothable, K-stable Q-Fano varieties. We also investigate the behavior of twisted Kahler-Ricci solitons in the Gromov-Hausdorff topology under this smoothing family.

Citations

• Degeneration of Kahler-Ricci solitons on Fano manifolds
• Bounding diameter of singular Kähler metric
• On the Yau-Tian-Donaldson conjecture for singular Fano varieties
• Monge-Ampère equations in big cohomology classes

Related

• Compactness of Kahler-Ricci solitons on Fano manifolds
• Twisted and conical Kähler-Ricci soliton on Fano manifolds
• Kähler-Ricci solitons on toric Fano orbifolds
• Fano manifolds with weak almost Kähler-Ricci solitons
• Degeneration of Kahler-Ricci solitons on Fano manifolds