K-stability of Fano varieties via admissible flags

Abban, Hamid; Zhuang, Ziquan

Abstract

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.

Citation

Abban, H., & Zhuang, Z. (2022). K-stability of Fano varieties via admissible flags. Forum of Mathematics, Pi, 10, Article e15. https://doi.org/10.1017/fmp.2022.11

• Journal Article Type: Article
• Acceptance Date: Jun 1, 2022
• Online Publication Date: Jun 30, 2022
• Publication Date: Jun 30, 2022
• Deposit Date: Mar 17, 2025
• Publicly Available Date: Mar 18, 2025
• Journal: Forum of Mathematics, Pi
• Print ISSN: 2050-5086
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 10
• Article Number: e15
• DOI: https://doi.org/10.1017/fmp.2022.11
• Keywords: K-stability, Fano varieties
• Public URL: https://nottingham-repository.worktribe.com/output/46731433
• Publisher URL: https://www.cambridge.org/core/journals/forum-of-mathematics-pi/article/kstability-of-fano-varieties-via-admissible-flags/230599DCAB515D0E8569EE6D2C2F9C70
• Additional Information: Copyright: © The Author(s), 2022. Published by Cambridge University Press; License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.; Free to read: This content has been made available to all.