Asymptotic Chow stability of uniformly K-stable toric varieties

2024/05/11 by King Leung Lee, Lee, King leung, Naoto Yotsutani +1
Mathematics · Physics and Astronomy · #14M25 #51M20 #53C55 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2405.06883

openalex publication_date 2024/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

For a polarized toric variety, we provide a sufficient criterion ensuring that a uniformly K-stable polarized toric variety (X,L) is asymptotically Chow polystable, under the assumption that the obstruction to asymptotic Chow semistability (the Futaki-Ono invariant) vanishes. Our approach is based on a detailed study of triangulations of neighborhoods of the vertices of the associated moment polytope Δ. As an application, we prove that every uniformly K-stable polarized smooth toric variety (X,L) with vanishing Futaki-Ono invariant is asymptotically Chow polystable.

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