Remarks on modified Ding functional for toric Fano manifolds

2017/10/18 by Satoshi Nakamura, Nakamura, Satoshi
Mathematics · #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.1710.06828

openalex publication_date 2017/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a characterization of relative Ding stable toric Fano manifolds in terms of the behavior of the modified Ding functional. We call the corresponding behavior of the modified Ding functional the pseudo-boundedness from below. We also discuss the pseudo-boundedness of the Ding / Mabuchi functional of general Fano manifolds.

Citations

• Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds
• KÄHLER GEOMETRY OF TORIC VARIETIES AND EXTREMAL METRICS
• Mabuchi metrics and properness of the modified DING functional

Related

• Relative Ding and K-stability of toric Fano manifolds in low dimensions
• On the coupled Ding stability and the Yau--Tian--Donaldson correspondence for Fano manifolds
• Mabuchi metrics and properness of the modified DING functional
• Stability of anti-canonically balanced metrics
• Tian's stabilization problem for toric Fanos