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 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.
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