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math.CV2025
Singular cscK metrics on smoothable varieties
Chung-Ming Pan, Tat Dat Tô, Antonio Trusiani
We prove the lower semi-continuity of the coercivity threshold of Mabuchi functional along a degenerate family of normal compact Kähler varieties with klt singularities. Moreover,…
math.CV2024
Demailly-Lelong numbers on complex spaces
Chung-Ming Pan
We prove a conjecture proposed by Berman-Boucksom-Eyssidieux-Guedj-Zeriahi, affirming that the Demailly-Lelong number can be determined through a combination of intersection number…
math.CV2024
Kähler-Einstein metrics on families of Fano varieties
Chung-Ming Pan, Antonio Trusiani
Given a one-parameter family of -Fano varieties such that the central fibre admits a unique Kähler-Einstein metric, we provide an analytic method to show that the neig…