The Uniform Version of Yau–Tian–Donaldson Conjecture for Singular Fano Varieties
By Chi Li, G. Tian, Feng Wang. Peking Mathematical Journal, 2019
75 citations recorded by the source corpus.
We prove the following result: if a $$\,\,\,\,\,{\mathbb {Q}}\,\,\,\,\,$$ Q -Fano variety is uniformly K-stable, then it admits a Kähler–Einstein metric. This proves the uniform version of Yau–Tian–Donaldson conjecture for all (singular) Fano varieties with discrete automorphism groups. We achieve this by modifying Berman–Boucksom–Jonsson’s strategy in the smooth case with appropriate perturbative arguments. This perturbation approach depends on the valuative criterion and non-Archimedean estimates, and is motivated by our previous paper.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b564e23315db5dc71aed8828cfe4d9101f7b2691
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In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Geodesic rays and stability in the cscK problem (2020, methodology): “The proof in [52] depends on earlier works of Berman-Boucksom-Jonsson ([5]), Hisamoto ([49]) and our perturbative approach in [54], and uses a new valuative criterion for G-uniform stability.”
- K-stability of Fano varieties: an algebro-geometric approach (2020, result): “red by a non-Archimedean geometry viewpoint. This is indeed conceptually closely related to the foundational progress that people made to understand K-stability in the algebraic side. As a result, in [LTW19] and [Li19] the approach of in [BBJ18] was fully carried out, and it was proved that a Q-Fano”
- On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations (2020, methodology): “ξ = Θ = 0), [33, 25, 9, 37, 73, 58, 81] for the twisted/conical Kähler-Einstein case (i.”