Sasaki–Einstein metrics and K–stability
© 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 c...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Mathematical Sciences Publishers
2022
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| Online Access: | https://hdl.handle.net/1721.1/145629 |
| Summary: | © 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. |
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