Sasaki–Einstein metrics and K–stability
Name
1512.07213.pdf
Description
Submitted version
Size
593 KB
Format
Adobe PDF
Checksum (MD5)
ed280e48b12467ffc4bc666d9b102c97
Author(s)
Collins, Tristan
Székelyhidi, Gábor
Date Issued
2019
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.2140/GT.2019.23.1339
