CM Stability And The Generalized Futaki Invariant II

2006/06/20 by Sean Timothy Paul, Gang Tian, Paul, Sean Timothy +1 · 3 citations
Mathematics · Physics and Astronomy · #14D06 (Secondary) #53C55 (Primary) #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0606505

openalex publication_date 2006/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Mabuchi K-energy map is exhibited as a singular metric on the refined CM polarization of any equivariant family X\oversetp→ S. Consequently we show that the generalized Futaki invariant is the leading term in the asymptotics of the reduced K-energy of the generic fiber of the map p. Properness of the K-energy implies that the generalized Futaki invariant is strictly negative.

Cited by

• A YTD correspondence for constant scalar curvature metrics
• Uniform K-stability, Duistermaat-Heckman measures and singularities of\n pairs
• Equivariant CM minimization for extremal manifolds

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