The existence of the Kähler–Ricci soliton degeneration-Reference-Cited by-同舟云学术

The existence of the Kähler–Ricci soliton degeneration

Published:2023 Issue: Volume:11 Page:
ISSN:2050-5086
Container-title:Forum of Mathematics, Pi
language:en
Short-container-title:Forum of Mathematics, Pi

Author:

Blum Harold^ORCID,Liu Yuchen^ORCID,Xu Chenyang^ORCID,Zhuang Ziquan^ORCID

Abstract

Abstract We prove an algebraic version of the Hamilton–Tian conjecture for all log Fano pairs. More precisely, we show that any log Fano pair admits a canonical two-step degeneration to a reduced uniformly Ding stable triple, which admits a Kähler–Ricci soliton when the ground field

Publisher

Cambridge University Press (CUP)

Subject

Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Analysis

Reference51 articles.

1. Kähler–Ricci solitons on toric manifolds with positive first Chern class

2. Kähler–Ricci flow, Kähler–Einstein metric, and K–stability

3. A minimizing valuation is quasi-monomial

4. Uniqueness of the minimizer of the normalized volume function

5. K-semistability is equivariant volume minimization

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Kähler–Ricci Flow on $${\textbf{G}}$$-Spherical Fano Manifolds;Peking Mathematical Journal;2024-08-13

2. A non-Archimedean approach to K-stability, I: Metric geometry of spaces of test configurations and valuations;Annales de l'Institut Fourier;2024-07-03

3. Convexity of multiplicities of filtrations on local rings;Compositio Mathematica;2024-03-13

4. Algebraic uniqueness of Kähler–Ricci flow limits and optimal degenerations of Fano varieties;Geometry & Topology;2024-03-13

5. A non-Archimedean approach to K-stability, II: Divisorial stability and openness;Journal für die reine und angewandte Mathematik (Crelles Journal);2023-10-28