Titlebook: Birational Geometry, K?hler–Einstein Metrics and Degenerations; Moscow, Shanghai and Ivan Cheltsov,Xiuxiong Chen,Jihun Park Conference proc

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A Note on Families of K-Semistable Log-Fano Pairs,d of the nefness threeshold for the log-anti-canonical line bundle on families of K-stable log Fano pairs. We also prove a bound on the multiplicity of fibers for families of K-semistable log Fano varieties, which to the best of our knowledge is new.

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,Generalized Thomas–Yau Uniqueness Theorems,Lagrangians in K?hler–Einstein manifolds or more generally .-minimal Lagrangians introduced by Lotay and Pacini [13,14]. In every case the heart of the proof is to make certain Hamiltonian perturbations. For this we use the method by Imagi, Joyce and Oliveira dos Santos [8,Theorem 4.7].

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Stephanie Margarete Müller,Martin GrunwaldWe prove that a Kawamata log terminal pair has the canonical model.

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