## Geometry & Topology

### Sasaki–Einstein metrics and K–stability

#### Abstract

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

#### Article information

Source
Geom. Topol., Volume 23, Number 3 (2019), 1339-1413.

Dates
Revised: 11 July 2018
Accepted: 8 August 2018
First available in Project Euclid: 5 June 2019

https://projecteuclid.org/euclid.gt/1559700275

Digital Object Identifier
doi:10.2140/gt.2019.23.1339

Mathematical Reviews number (MathSciNet)
MR3956894

Zentralblatt MATH identifier
07079060

Keywords
K–stability Kähler–Einstein Sasaki

#### Citation

Collins, Tristan C; Székelyhidi, Gábor. Sasaki–Einstein metrics and K–stability. Geom. Topol. 23 (2019), no. 3, 1339--1413. doi:10.2140/gt.2019.23.1339. https://projecteuclid.org/euclid.gt/1559700275

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