63 citations · 275 across the 28 of their papers we have counts for
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math.AG2021★ 16 cited
The existence of the Kähler-Ricci soliton degeneration
Harold Blum, Yuchen Liu, Chenyang Xu +1
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 r…
math.AG2021★ 12 cited
Finite generation for valuations computing stability thresholds and applications to K-stability
Yuchen Liu, Chenyang Xu, Ziquan Zhuang
We prove that on any log Fano pair of dimension whose stability threshold is less than , any valuation computing the stability threshold has a finitely generated…
math.AG2021★ 2 cited
Seshadri constants and K-stability of Fano manifolds
Hamid Abban, Ziquan Zhuang
We give a lower bound of the -invariants of ample line bundles in terms of Seshadri constants. As applications, we prove the uniform K-stability of infinitely many families of F…