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The existence of the K\"ahler-Ricci soliton degeneration

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arxiv 2103.15278 v2 pith:BFXSTZNZ submitted 2021-03-29 math.AG math.DG

classification math.AGmath.DG
keywords admitsahler-riccidegenerationfanomathbbsolitonalgebraiccanonical
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abstract

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 $\mathbb{k}=\mathbb{C}$.

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