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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.AG2020★ 14 cited
Uniqueness of the minimizer of the normalized volume function
Chenyang Xu, Ziquan Zhuang
We confirm a conjecture of Chi Li which says that the minimizer of the normalized volume function for a klt singularity is unique up to rescaling. This is achieved by defining stab…
math.AG2017★ 2 cited
Interaction Between Singularity Theory and the Minimal Model Program
Chenyang Xu
We survey some recent topics on singularities, with a focus on their connection to the minimal model program. This includes the construction and properties of dual complexes, the p…