Sasaki–Einstein metrics and K–stability

Author(s)
Collins, Tristan; Székelyhidi, Gábor
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Abstract
© 2019, Mathematical Sciences Publishers. All rights reserved. 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.
Date issued
2019
URI
https://hdl.handle.net/1721.1/145629
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Geometry and Topology
Publisher
Mathematical Sciences Publishers
Citation
Collins, Tristan and Székelyhidi, Gábor. 2019. "Sasaki–Einstein metrics and K–stability." Geometry and Topology, 23 (3).
Version: Original manuscript
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