Degeneration of Kahler-Ricci solitons on Fano manifolds

2012/11/26 by D. H. Phong, Jian Song, Phong, D. H. +3 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1211.5849

openalex publication_date 2012/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the space KR(n,F) of Kahler-Ricci solitons on n-dimensional Fano manifolds with Futaki invariant bounded by F. We prove a partial C⁰ estimate for KR(n,F) as a generalization of the recent work of Donaldson-Sun for Fano Kahler-Einstein manifolds. In particular, any sequence in KR(n,F) has a convergent subsequence in the Gromov-Hausdorff topology to a Kahler- Ricci soliton on a Q-Fano variety with log terminal singularities.

Cited by

• Existence of Kahler-Ricci solitons on smoothable Q-Fano varities
• Regularity of Kähler-Ricci flows on Fano manifolds
• Almost soliton duality

Related

• Compactness of Kahler-Ricci solitons on Fano manifolds
• Fano manifolds with weak almost Kähler-Ricci solitons
• 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 Kähler-Ricci solitons