The existence of the Kähler–Ricci soliton degeneration

DOI10.1017/fmp.2023.5OpenAlexW3151794603MaRDI QIDQ5887135

Yuchen Liu, Harold Blum, Ziquan Zhuang, Chen Yang Xu

Publication date: 17 April 2023

Published in: Forum of Mathematics, Pi (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.15278

Mathematics Subject Classification ID

Fano varieties (14J45) Kähler-Einstein manifolds (32Q20) Birational geometry (14E99)

Related Items (4)

A non-Archimedean approach to K-stability. II: Divisorial stability and openness ⋮ Equivariant \(\mathbb{R}\)-test configurations and semistable limits of \(\mathbb{Q}\)-Fano group compactifications ⋮ Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties ⋮ Convexity of multiplicities of filtrations on local rings

Cites Work

• Unnamed Item
• Unnamed Item
• K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
• Kähler-Einstein metrics along the smooth continuity method
• Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory
• Regularity of Kähler-Ricci flows on Fano manifolds
• Boundedness of weak Fano pairs with alpha-invariants and volumes bounded below
• Kähler-Einstein metrics with positive scalar curvature
• The analysis of linear partial differential operators. I: Distribution theory and Fourier analysis.
• Convergence of Ricci flows with bounded scalar curvature
• K-semistability is equivariant volume minimization
• Uniform \(K\)-stability, Duistermaat-Heckman measures and singularities of pairs
• Kähler-Ricci flow, Kähler-Einstein metric, and K-stability
• Kähler--Ricci solitons on toric manifolds with positive first Chern class
• Valuations and asymptotic invariants for sequences of ideals
• On the birational automorphisms of varieties of general type
• Basis divisors and balanced metrics
• Distribution of logarithmic spectra of the equilibrium energy
• Uniqueness of the minimizer of the normalized volume function
• \(G\)-uniform stability and Kähler-Einstein metrics on Fano varieties
• Openness of K-semistability for Fano varieties
• Plurisubharmonic geodesics in spaces of non-Archimedean metrics of finite energy
• Finite generation for valuations computing stability thresholds and applications to K-stability
• A minimizing valuation is quasi-monomial
• Space of Ricci flows. II. Part B: Weak compactness of the flows
• The Kähler-Ricci flow and optimal degenerations
• On positivity of the CM line bundle on K-moduli spaces
• Spaces of norms, determinant of cohomology and Fekete points in non-Archimedean geometry
• Special test configuration and \(K\)-stability of Fano varieties
• Thresholds, valuations, and K-stability
• A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry
• A valuative criterion for uniform K-stability of \(\mathbb{Q}\)-Fano varieties
• Kähler-Ricci soliton and \(H\)-functional
• Perelman’s entropy and Kähler-Ricci flow on a Fano manifold
• A Guided Tour to Normalized Volume
• Boundedness of Q-Fano varieties with degrees and alpha-invariants bounded from below
• Existence of minimal models for varieties of log general type
• Restricted volumes and base loci of linear series
• Convex bodies associated to linear series
• K-STABILITY OF FANO MANIFOLDS WITH NOT SMALL ALPHA INVARIANTS
• Introduction
• Towards finite generation of higher rational rank valuations
• Openness of uniform K-stability in families of $Q$-Fano varieties
• K-stability of Fano varieties via admissible flags
• Algebraicity of the metric tangent cones and equivariant K-stability
• Okounkov bodies of filtered linear series

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