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...
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| 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 |
| _version_ | 1826214925837533184 |
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| author | Collins, Tristan Székelyhidi, Gábor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Collins, Tristan Székelyhidi, Gábor |
| author_sort | Collins, Tristan |
| collection | MIT |
| description | © 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. |
| first_indexed | 2024-09-23T16:13:22Z |
| format | Article |
| id | mit-1721.1/145629 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:13:22Z |
| publishDate | 2022 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | mit-1721.1/1456292022-10-04T03:03:23Z Sasaki–Einstein metrics and K–stability Collins, Tristan Székelyhidi, Gábor Massachusetts Institute of Technology. Department of Mathematics © 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. 2022-09-30T16:44:31Z 2022-09-30T16:44:31Z 2019 2022-09-30T16:42:11Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/145629 Collins, Tristan and Székelyhidi, Gábor. 2019. "Sasaki–Einstein metrics and K–stability." Geometry and Topology, 23 (3). en 10.2140/GT.2019.23.1339 Geometry and Topology Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Mathematical Sciences Publishers arXiv |
| spellingShingle | Collins, Tristan Székelyhidi, Gábor Sasaki–Einstein metrics and K–stability |
| title | Sasaki–Einstein metrics and K–stability |
| title_full | Sasaki–Einstein metrics and K–stability |
| title_fullStr | Sasaki–Einstein metrics and K–stability |
| title_full_unstemmed | Sasaki–Einstein metrics and K–stability |
| title_short | Sasaki–Einstein metrics and K–stability |
| title_sort | sasaki einstein metrics and k stability |
| url | https://hdl.handle.net/1721.1/145629 |
| work_keys_str_mv | AT collinstristan sasakieinsteinmetricsandkstability AT szekelyhidigabor sasakieinsteinmetricsandkstability |