Compactness of Kähler-Ricci solitons on Fano manifolds (Q2074857)

The authors extend a result of \textit{D. H. Phong} et al. [Zesz. Nauk. Uniw. Jagiell., Univ. Iagell. Acta Math. 52, 29--43 (2015; Zbl 1360.53049)] on degeneration of Fano Kähler-Ricci solitons which remove the assumption on the uniform bound of the Futaki invariant. Let \(\mathcal{KR}(n)\) be the space of Kähler-Ricci solitons on \(n\)-dimensional Fano manifolds. The authors prove that any sequence in \(\mathcal{KR}(n)\) has a subsequence which converges in the Gromov-Hausdorff topology to a Kähler-Ricci soliton on an \(n\)-dimensional \(\mathbb{Q}\)-Fano variety with log terminal singularities.