Degeneration of Kahler-Ricci solitons on Fano manifolds

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 C^0 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.

References in corpus (2)

• Kahler-Einstein metrics and stability
• Degeneration of Kähler-Ricci solitons

Cited by in corpus (7)

• Riemannian geometry of Kahler-Einstein currents
• Extremal Kähler metrics
• Kähler-Einstein metrics along the smooth continuity method
• Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
• Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below, II
• Riemannian geometry of Kahler-Einstein currents III: compactness of Kahler-Einstein manifolds of negative scalar curvature
• Regularity of Kähler-Ricci flow