Sasaki–Einstein metrics and K–stability

By Tristan C. Collins, G'abor Sz'ekelyhidi. Geometry and Topology, 2015

100 citations recorded by the source corpus.

We show that a polarized affine variety admits a Ricci flat K\"ahler cone metric, if and only if it is K-stable. This generalizes Chen-Donaldson-Sun's solution of the Yau-Tian-Donaldson conjecture to K\"ahler cones, or equivalently, Sasakian manifolds. As an application we show that the five-sphere admits infinitely many families of Sasaki-Einstein metrics.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/565a9d57171126755b4c87b2faabcb8df04bed8a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Chi Li
2. Xiaowei Wang
3. Yuchen Liu
4. H. Blum
5. Chenyang Xu
6. Ziquan Zhuang
7. Mattias Jonsson
8. Kento Fujita

In Geometry and Topology

1. Chi Li
2. Yuchen Liu
3. Xiaowei Wang
4. H. Blum
5. Chenyang Xu
6. Ziquan Zhuang
7. Mattias Jonsson
8. Kento Fujita

Citations in the corpus

• Stability of Valuations: Higher Rational Rank (2017, methodology): “e−r2dV Xt = Cn · Z {r≤1}∩Xt e−r2dV Xt . (80) Now on the part X ∩ ({r≤ 1} × C) ⊂ CN × C, we can then use the same calculation as in [Li17a, section 4] to get the conclusion. Proposition 5.14 (see also [CS15]). If AX(ξ0) = n, then the asymptotic slope of the Ding energy is equal to the Futaki invarian”
• Algebraicity of the metric tangent cones and equivariant K-stability (2018, methodology): “y special test configurations with vanishing Futaki invariants must already be special. To apply this to metric tangent cones which are Ricciflat Ka¨hler cones, we use the result of Colins-Sz´ekelyhidi [CS19] about the K-polystability of Ricci-flat Kahler cones. Since we need to allow more general test”
• Kähler–Einstein metrics and volume minimization (2016, methodology): “1. The rest of this section is devoted to the proof of Theorem 6.2. The idea of proof for the irregular case is to use approximation by quasi-regular ones, similar to the one used in [CS12] (see also [CS15]). If ξ = J(r∂r) is a quasi-regular Reeb vector field, then the holomorphic field u = r∂r− iξ ge”