K-stability of Fano varieties via admissible flags
We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces at generalised Eckardt points and for cubic su...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2022-01-01
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| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508622000117/type/journal_article |
| _version_ | 1811156250521501696 |
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| author | Hamid Abban Ziquan Zhuang |
| author_facet | Hamid Abban Ziquan Zhuang |
| author_sort | Hamid Abban |
| collection | DOAJ |
| description | We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces at generalised Eckardt points and for cubic surfaces at all points, and (c) provide a new algebraic proof of Tian’s criterion for K-stability, amongst other applications. |
| first_indexed | 2024-04-10T04:48:29Z |
| format | Article |
| id | doaj.art-9e1b1c955e444acf9338b40d9143ec33 |
| institution | Directory Open Access Journal |
| issn | 2050-5086 |
| language | English |
| last_indexed | 2024-04-10T04:48:29Z |
| publishDate | 2022-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj.art-9e1b1c955e444acf9338b40d9143ec332023-03-09T12:34:22ZengCambridge University PressForum of Mathematics, Pi2050-50862022-01-011010.1017/fmp.2022.11K-stability of Fano varieties via admissible flagsHamid Abban0https://orcid.org/0000-0002-4260-3243Ziquan Zhuang1https://orcid.org/0000-0002-5466-5206Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UKDepartment of Mathematics, MIT, Cambridge, MA, 02139, USA; E-mail:We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces at generalised Eckardt points and for cubic surfaces at all points, and (c) provide a new algebraic proof of Tian’s criterion for K-stability, amongst other applications.https://www.cambridge.org/core/product/identifier/S2050508622000117/type/journal_articleK-stabilityFano varieties14J4532Q20 |
| spellingShingle | Hamid Abban Ziquan Zhuang K-stability of Fano varieties via admissible flags Forum of Mathematics, Pi K-stability Fano varieties 14J45 32Q20 |
| title | K-stability of Fano varieties via admissible flags |
| title_full | K-stability of Fano varieties via admissible flags |
| title_fullStr | K-stability of Fano varieties via admissible flags |
| title_full_unstemmed | K-stability of Fano varieties via admissible flags |
| title_short | K-stability of Fano varieties via admissible flags |
| title_sort | k stability of fano varieties via admissible flags |
| topic | K-stability Fano varieties 14J45 32Q20 |
| url | https://www.cambridge.org/core/product/identifier/S2050508622000117/type/journal_article |
| work_keys_str_mv | AT hamidabban kstabilityoffanovarietiesviaadmissibleflags AT ziquanzhuang kstabilityoffanovarietiesviaadmissibleflags |