Valuative invariants with higher moments

2020/12/09 by Kewei Zhang, Zhang, Kewei
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2012.04856

openalex publication_date 2020/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we introduce a family of valuative invariants defined in terms of the p-th moment of the expected vanishing order. These invariants lie between α and δ-invariants. They vary continuously in the big cone and semi-continuously in families. Most importantly, they can detect the K-stability of Fano varieties, which generalizes the α and δ-criterions in the literature. They are also related to the d_p-geometry of maximal geodesic rays.

Citations

• A non-Archimedean approach to K-stability
• Monge-Ampère equations in big cohomology classes

Related

• Invariants of Varieties and Singularities inspired by Kahler-Einstein problems
• Valuative stability of polarised varieties
• A non-Archimedean approach to K-stability, II: divisorial stability and openness
• Stability thresholds for big classes
• Seshadri constants and K-stability of Fano manifolds