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Sasaki–Einstein metrics
and K–stability
Tristan C Collins and Gábor Székelyhidi |
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Geometry & Topology 23 (2019) 1339–1413
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Abstract |
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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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Keywords
K–stability, Kähler–Einstein, Sasaki
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Mathematical Subject Classification 2010
Primary: 32Q20, 53C25
Secondary: 32Q26
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References |
Publication
Received: 25 September 2017
Revised: 11 July 2018
Accepted: 8 August 2018
Published: 28 May 2019
Proposed: Simon Donaldson
Seconded: John Lott, Tobias H Colding
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Authors |
| Tristan C Collins | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| Gábor Székelyhidi | |
| Department of Mathematics University of Notre Dame Notre Dame, IN United States |
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