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2019 Sasaki–Einstein metrics and K–stability
Tristan C Collins, Gábor Székelyhidi
Geom. Topol. 23(3): 1339-1413 (2019). DOI: 10.2140/gt.2019.23.1339

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.

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Tristan C Collins. Gábor Székelyhidi. "Sasaki–Einstein metrics and K–stability." Geom. Topol. 23 (3) 1339 - 1413, 2019. https://doi.org/10.2140/gt.2019.23.1339

Information

Received: 25 September 2017; Revised: 11 July 2018; Accepted: 8 August 2018; Published: 2019
First available in Project Euclid: 5 June 2019

zbMATH: 07079060
MathSciNet: MR3956894
Digital Object Identifier: 10.2140/gt.2019.23.1339

Subjects:
Primary: 32Q20, 53C25
Secondary: 32Q26

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.23 • No. 3 • 2019
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