Openness of K-semistability for Fano varieties

2019/07/04 by Harold Blum, Yuchen Liu, Blum, Harold +3 · 3 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1907.02408

openalex publication_date 2019/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also prove that any special test configuration arises from a log canonical place of a bounded complement and establish properties of any minimizer of the stability threshold.

Cited by

• K-Moduli of Fano Threefolds of Family 3.3
• Asymptotically flat divisors and strongly F-regular type varieties
• Finite generation of higher rank quasi-monomial valuations via the extended Rees algebra

Related

• Openness of uniform K-stability in families of ℚ-Fano varieties
• K-semistability of log Fano cone singularities
• A valuative criterion of K-polystability
• Special test configurations and K-stability of Fano varieties
• Finite generation for valuations computing stability thresholds and applications to K-stability