The existence of the Kähler–Ricci soliton degeneration
The existence of the Kähler–Ricci soliton degeneration
We prove an algebraic version of the Hamilton-Tian Conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a reduced uniformly Ding stable triple, which admits a K\"ahler-Ricci soliton when the ground field $\mathbb{k}=\mathbb{C}$.