A valuative criterion for uniform K-stability of $\mathbb{Q}$-Fano varieties

Abstract

We give a simple necessary and sufficient condition for uniform K-stability of $\mathbb{Q}$-Fano varieties.

35 pages, minor revision; add Section 6 and references

References in corpus (8)

• A variational approach to the Yau-Tian-Donaldson conjecture
• K-stability of constant scalar curvature polarization
• A stronger concept of K-stability
• Stability of Valuations and Kollár Components
• Optimal bounds for the volumes of Kähler-Einstein Fano manifolds
• Extremal metrics and K-stability (PhD thesis)
• Kähler-Einstein metrics and volume minimization
• Examples of K-unstable Fano manifolds with the Picard number one

Cited by in corpus (11)

• A non-Archimedean approach to K-stability
• Stability of Valuations and Kollár Components
• Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces
• Openness of uniform K-stability in families of $\mathbb{Q}$-Fano varieties
• Birational superrigidity and K-stability of Fano complete intersections of index one (with an appendix written jointly with Charlie Stibitz)
• Birational superrigidity and K-stability of singular Fano complete intersections
• On the Yau-Tian-Donaldson conjecture for singular Fano varieties
• Uniqueness of K-polystable degenerations of Fano varieties
• K-stability of Fano manifolds with not small alpha invariants
• Asymptotic Chow semistability implies Ding polystability for Gorenstein toric Fano varieties
• The Kähler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations