Finiteness of K-moduli compactifications

2025/09/19 by Chuyu Zhou, Zhou, Chuyu
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2509.15728

openalex publication_date 2025/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we aim to prove the finite semi-algebraic chamber decomposition theorem for K-semi(poly)stability under the assumption of the log boundedness of K-semistable degenerations. This boundedness assumption is naturally arising from the finiteness of K-moduli compactifications.

Citations

• Variation of cones of divisors in a family of varieties -- Fano type case
• The K-moduli space of a family of conic bundle threefolds
• Finite generation for valuations computing stability thresholds and applications to K-stability
• Wall crossing for K-moduli spaces of plane curves
• Algebraicity of the Metric Tangent Cones and Equivariant K-stability
• Special test configurations and K-stability of Fano varieties

Related

• On log minimality of weak K-moduli compactifications of Calabi-Yau varieties
• Non-proportional wall crossing for K-stability
• Semi-toric and toroidal compactifications as log minimal models, and applications to weak K-moduli
• Two results regarding the variation of K-moduli
• On properness of K-moduli spaces and optimal degenerations of Fano varieties