Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds
By Chi Li. 2013
60 citations recorded by the source corpus.
In this note, using the recent compactness results of Tian and Chen-Donaldson-Sun, we prove the K-semistable version of Yau-Tian-Donaldson correspondence for Fano manifolds.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e88debacccf429030c4e01308e8b79169d75700e
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Algebraicity of the metric tangent cones and equivariant K-stability (2018, methodology): “Theorem 2.5 ([Li17, LL16, LX16, LX17]).”
- Stability of valuations and Kollár components (2016, methodology): “(14) If φ : Ṽ → V is a model that contains E as a divisor, then v can also be obtained as a quasi-monomial valuation on the model Ỹ → Y where Ỹ = Y ×V Ṽ (see [Li17b, Definition 6.12]).”
- Kähler–Einstein metrics and volume minimization (2016, background): “By the construction in [43,40] (see also [41, Section 5.”
- Stability of Valuations: Higher Rational Rank (2017, methodology): “Futaki invariant Fut(X0,D0,ξ0;η) ≥ 0, where (X0,D0) is the induced special degeneration by Sand η= −ξS. The following purely algebro-geometric statement can be seen as a generalization of a result in [Li17a], which was proved there by an analytic method. Proposition 3.7. Let (X,D,ξ0) be a log Fano c”
- Uniform stability of twisted constant scalar curvature K\"ahler metrics (2014, background): “By a recent result of Li, this conjecture is true in the case β = 1 [25].”
- A variational approach to the Yau–Tian–Donaldson conjecture (2015, background): “dix of [CRZ18], as a consequence of [LS14, SW16] (see also [Li11] for the toric case and [Cab18] for the case of Fano -manifolds of complexity one). The nal statement was also previously obtained in [Li17a], also building on [CDS15]. Proof of Theorem 7.5. We obviously have (X;L) s (X;L). Consider rs”
- Tropical and non-Archimedean limits of degenerating families of volume forms (2016, background): “When d = 0, this implies the following slight generalization of [Li15, Lem.”
- Minimizing normalized volumes of valuations (2015, background): “P3), then the associated pair (Pn−1, (1 − 1 k )D) is log-K-semistable but not log-K-polystable by [LS14, Li13].”
- K-semistability is equivariant volume minimization (2015, methodology): “Indeed by Izumi’s theorem in [Li13, Proposition 1.2] (see also [Izu85, Ree89, BFJ12]), there exist c1, c2 ∈ (0,+∞) such that c1v0 ≤ v1 ≤ c2v0.”
- Existence and deformations of Kähler–Einstein metrics on smoothable $\mathbb{Q}$-Fano varieties (2014, methodology): “0 − X i aiEi (2.9) for some positive integers ai, then we have KX˜/C = µ ∗K X/C + X i (ai−bi)Ei. (2.10) From this equation and the definition of relative canonical line bundle one can calculate, as in [30], the behavior of µ∗volh t in a neighborhood of a point ˜x∈ X0′ ∪ S iEi. There are three cases 1”